@article{MTMT:36462559,
title = {Selected topics from the theory of intersections of balls},
url = {https://m2.mtmt.hu/api/publication/36462559},
author = {Bezdek, Károly and Lángi, Zsolt and Naszódi, Márton},
doi = {10.1016/j.dam.2025.11.040},
journal-iso = {DISCRETE APPL MATH},
journal = {DISCRETE APPLIED MATHEMATICS},
volume = {382},
unique-id = {36462559},
issn = {0166-218X},
year = {2026},
eissn = {1872-6771},
pages = {60-82},
orcid-numbers = {Bezdek, Károly/0000-0003-3097-0430; Lángi, Zsolt/0000-0002-5999-5343; Naszódi, Márton/0000-0002-4194-0205}
}
@article{MTMT:36954782,
title = {Helly numbers for quantitative Helly-type results},
url = {https://m2.mtmt.hu/api/publication/36954782},
author = {Ivanov, G. and Naszódi, Márton},
doi = {10.1016/j.jcta.2026.106160},
journal-iso = {J COMB THEORY A},
journal = {JOURNAL OF COMBINATORIAL THEORY SERIES A},
volume = {220},
unique-id = {36954782},
issn = {0097-3165},
abstract = {We obtain three Helly-type results. First, we establish a Quantitative Colorful Helly-type theorem with the optimal Helly number 2d concerning the diameter of the intersection of a family of convex bodies. Second, we prove a Quantitative Helly-type theorem with the optimal Helly number 2d+1 for the pointwise minimum of logarithmically concave functions. Finally, we present a colorful version of the latter result with Helly number (number of color classes) 3d+1; however, we have no reason to believe that this bound is sharp. © 2026 The Authors},
keywords = {John ellipsoid; log-concave function; Colorful Helly-type theorem},
year = {2026},
eissn = {1096-0899},
orcid-numbers = {Naszódi, Márton/0000-0002-4194-0205}
}
@misc{MTMT:36868638,
title = {John Ellipsoids of Revolution},
url = {https://m2.mtmt.hu/api/publication/36868638},
author = {Grigory, Ivanov and Zsolt, Lángi and Naszódi, Márton and Ádám, Sagmeister},
unique-id = {36868638},
year = {2025},
orcid-numbers = {Naszódi, Márton/0000-0002-4194-0205}
}
@article{MTMT:35812525,
title = {Quantitative Steinitz theorem: a spherical version},
url = {https://m2.mtmt.hu/api/publication/35812525},
author = {Ivanov, G. and Naszódi, Márton},
doi = {10.1007/s40590-025-00717-9},
journal-iso = {BOL SOC MAT MEX},
journal = {BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA},
volume = {31},
unique-id = {35812525},
issn = {1405-213X},
year = {2025},
eissn = {2296-4495},
orcid-numbers = {Naszódi, Márton/0000-0002-4194-0205}
}
@article{MTMT:36425185,
title = {Quantitative Helly-type problems},
url = {https://m2.mtmt.hu/api/publication/36425185},
author = {Naszódi, Márton},
doi = {10.1007/s10476-025-00127-z},
journal-iso = {ANAL MATH},
journal = {ANALYSIS MATHEMATICA},
volume = {50},
unique-id = {36425185},
issn = {0133-3852},
abstract = {Quantitative versions of Helly's and Steinitz' theorems were first introduced by Bárány, Katchalski and Pach in 1982, and have grown into a well-studied field within discrete and convex geometry in the last decade. This note is an invitation to the field in the form of an incomplete collection of open problems.},
year = {2025},
eissn = {1588-273X},
pages = {1421-1428},
orcid-numbers = {Naszódi, Márton/0000-0002-4194-0205}
}
@article{MTMT:36339103,
title = {Higher rank antipodality},
url = {https://m2.mtmt.hu/api/publication/36339103},
author = {Naszódi, Márton and Szilágyi, Zsombor and Weiner, Mihály},
doi = {10.1112/mtk.70046},
journal-iso = {MATHEMATIKA},
journal = {MATHEMATIKA},
volume = {71},
unique-id = {36339103},
issn = {0025-5793},
abstract = {Motivated by general probability theory, we say that the set in is antipodal of rank , if for any elements , there is an affine map from to the -dimensional simplex that maps bijectively onto the vertices of . For , it coincides with the well-studied notion of (pairwise) antipodality introduced by Klee. We consider the following natural generalization of Klee's problem on antipodal sets: What is the maximum size of an antipodal set of rank in ? We present a geometric characterization of antipodal sets of rank and adapting the argument of Danzer and Gr & uuml;nbaum originally developed for the case, we prove an upper bound which is exponential in the dimension. We show that this problem can be connected to a classical question in computer science on finding perfect hashes, and it provides a lower bound on the maximum size, which is also exponential in the dimension. By connecting rank- antipodality to -neighborly polytopes, we obtain another upper bound when .},
keywords = {Mathematics, Applied},
year = {2025},
eissn = {2041-7942},
orcid-numbers = {Naszódi, Márton/0000-0002-4194-0205}
}
@article{MTMT:34220786,
title = {On Helly numbers of exponential lattices},
url = {https://m2.mtmt.hu/api/publication/34220786},
author = {Ambrus, Gergely and Martin, Balko and Frankl, Nóra and Jung, Attila and Naszódi, Márton},
doi = {10.1016/j.ejc.2023.103884},
journal-iso = {EUR J COMBIN},
journal = {EUROPEAN JOURNAL OF COMBINATORICS},
volume = {116},
unique-id = {34220786},
issn = {0195-6698},
year = {2024},
eissn = {1095-9971},
orcid-numbers = {Ambrus, Gergely/0000-0003-1246-6601; Naszódi, Márton/0000-0002-4194-0205}
}
@article{MTMT:34429497,
title = {Quantitative Steinitz theorem: A polynomial bound},
url = {https://m2.mtmt.hu/api/publication/34429497},
author = {Ivanov, Grigory and Naszódi, Márton},
doi = {10.1112/blms.12965},
journal-iso = {B LOND MATH SOC},
journal = {BULLETIN OF THE LONDON MATHEMATICAL SOCIETY},
volume = {56},
unique-id = {34429497},
issn = {0024-6093},
abstract = {The classical Steinitz theorem states that if the origin belongs to the interior of the convex hull of a set , then there are at most points of whose convex hull contains the origin in the interior. Bárány, Katchalski, and Pach proved the following quantitative version of Steinitz's theorem. Let be a convex polytope in containing the standard Euclidean unit ball . Then there exist at most vertices of whose convex hull satisfies with . They conjectured that holds with a universal constant . We prove , the first polynomial lower bound on . Furthermore, we show that is not greater than .},
year = {2024},
eissn = {1469-2120},
pages = {796-802},
orcid-numbers = {Ivanov, Grigory/0000-0002-5021-3982; Naszódi, Márton/0000-0002-4194-0205}
}
@inproceedings{MTMT:33673716,
title = {On Helly numbers of exponential lattices},
url = {https://m2.mtmt.hu/api/publication/33673716},
author = {Ambrus, Gergely and M., Balko and Frankl, Nóra and Jung, Attila and Naszódi, Márton},
booktitle = {39th International Symposium on Computational Geometry (SoCG 2023)},
doi = {10.4230/LIPIcs.SoCG.2023.8},
unique-id = {33673716},
abstract = {Given a set S⊆R2S⊆R2, define the Helly number of SS, denoted by H(S)H(S), as the smallest positive integer NN, if it exists, for which the following statement is true: For any finite family FF of convex sets in~R2R2 such that the intersection of any NN or fewer members of~FF contains at least one point of SS, there is a point of SS common to all members of FF.
We prove that the Helly numbers of exponential lattices {αn :n∈N0}2{αn:n∈N0}2 are finite for every α>1α>1 and we determine their exact values in some instances. In particular, we obtain H({2n :n∈N0}2)=5H({2n:n∈N0}2)=5, solving a problem posed by Dillon (2021).
For real numbers α,β>1α,β>1, we also fully characterize exponential lattices L(α,β)={αn :n∈N0}×{βn :n∈N0}L(α,β)={αn:n∈N0}×{βn:n∈N0} with finite Helly numbers by showing that H(L(α,β))H(L(α,β)) is finite if and only if logα(β)logα(β) is rational.},
keywords = {Set theory; Positive integers; Convex set; Integer-N; Diophantine approximation; Lattice L; EXPONENTIALS; Helly number; Real number; exponential lattices; Helly numbers; Exponential lattice},
year = {2023},
orcid-numbers = {Ambrus, Gergely/0000-0003-1246-6601; Naszódi, Márton/0000-0002-4194-0205}
}
@article{MTMT:34772583,
title = {Functional John and Löwner Conditions for Pairs of Log-Concave Functions},
url = {https://m2.mtmt.hu/api/publication/34772583},
author = {Ivanov, Grigory and Naszódi, Márton},
doi = {10.1093/imrn/rnad210},
journal-iso = {INT MATH RES NOTICES},
journal = {INTERNATIONAL MATHEMATICS RESEARCH NOTICES},
volume = {2023},
unique-id = {34772583},
issn = {1073-7928},
abstract = {John’s fundamental theorem characterizing the largest volume ellipsoid contained in a convex body in has seen several generalizations and extensions. One direction, initiated by V. Milman is to replace ellipsoids by positions (affine images) of another body . Another, more recent direction is to consider logarithmically concave functions on instead of convex bodies: we designate some special, radially symmetric log-concave function as the analogue of the Euclidean ball, and want to find its largest integral position under the constraint that it is pointwise below some given log-concave function . We follow both directions simultaneously: we consider the functional question, and allow essentially any meaningful function to play the role of above. Our general theorems jointly extend known results in both directions. The dual problem in the setting of convex bodies asks for the smallest volume ellipsoid, called Löwner’s ellipsoid, containing . We consider the analogous problem for functions: we characterize the solutions of the optimization problem of finding a smallest integral position of some log-concave function under the constraint that it is pointwise above . It turns out that in the functional setting, the relationship between the John and the Löwner problems is more intricate than it is in the setting of convex bodies.},
year = {2023},
eissn = {1687-0247},
pages = {20613-20669},
orcid-numbers = {Naszódi, Márton/0000-0002-4194-0205}
}
@article{MTMT:32282957,
title = {An analogue of a theorem of Steinitz for ball polyhedra in R-3},
url = {https://m2.mtmt.hu/api/publication/32282957},
author = {Almohammad, Sami Mezal and Lángi, Zsolt and Naszódi, Márton},
doi = {10.1007/s00010-021-00815-9},
journal-iso = {AEQUATIONES MATH},
journal = {AEQUATIONES MATHEMATICAE},
volume = {96},
unique-id = {32282957},
issn = {0001-9054},
abstract = {Steinitz's theorem states that a graph G is the edge-graph of a 3-dimensional convex polyhedron if and only if, G is simple, plane and 3-connected. We prove an analogue of this theorem for ball polyhedra, that is, for intersections of finitely many unit balls in R-3.},
keywords = {Polyhedron; Steinitz's theorem; Ball polyhedron; Edge-graph},
year = {2022},
eissn = {1420-8903},
pages = {403-415},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343; Naszódi, Márton/0000-0002-4194-0205}
}
@article{MTMT:32750793,
title = {Functional John ellipsoids},
url = {https://m2.mtmt.hu/api/publication/32750793},
author = {Ivanov, Grigory and Naszódi, Márton},
doi = {10.1016/j.jfa.2022.109441},
journal-iso = {J FUNCT ANAL},
journal = {JOURNAL OF FUNCTIONAL ANALYSIS},
volume = {282},
unique-id = {32750793},
issn = {0022-1236},
year = {2022},
eissn = {1096-0783},
orcid-numbers = {Naszódi, Márton/0000-0002-4194-0205}
}
@article{MTMT:32838425,
title = {A Quantitative Helly-Type Theorem: Containment in a Homothet},
url = {https://m2.mtmt.hu/api/publication/32838425},
author = {Ivanov, Grigory and Naszódi, Márton},
doi = {10.1137/21M1403308},
journal-iso = {SIAM J DISCRETE MATH},
journal = {SIAM JOURNAL ON DISCRETE MATHEMATICS},
volume = {36},
unique-id = {32838425},
issn = {0895-4801},
year = {2022},
eissn = {1095-7146},
pages = {951-957},
orcid-numbers = {Naszódi, Márton/0000-0002-4194-0205}
}
@article{MTMT:32580843,
title = {Computing the covering radius of a polytope with an application to lonely runners},
url = {https://m2.mtmt.hu/api/publication/32580843},
author = {Jana, Cslovjecsek and Romanos, Diogenes Malikiosis and Naszódi, Márton and Matthias, Schymura},
doi = {10.1007/s00493-020-4633-8},
journal-iso = {COMBINATORICA},
journal = {COMBINATORICA},
volume = {42},
unique-id = {32580843},
issn = {0209-9683},
year = {2022},
eissn = {1439-6912},
pages = {463-490},
orcid-numbers = {Naszódi, Márton/0000-0002-4194-0205}
}
@article{MTMT:32192509,
title = {Quantitative Fractional Helly and (p, q)-Theorems},
url = {https://m2.mtmt.hu/api/publication/32192509},
author = {Jung, Attila and Naszódi, Márton},
doi = {10.1016/j.ejc.2021.103424},
journal-iso = {EUR J COMBIN},
journal = {EUROPEAN JOURNAL OF COMBINATORICS},
volume = {99},
unique-id = {32192509},
issn = {0195-6698},
year = {2022},
eissn = {1095-9971},
orcid-numbers = {Naszódi, Márton/0000-0002-4194-0205}
}
@article{MTMT:32819310,
title = {Covering Convex Bodies and the Closest Vector Problem},
url = {https://m2.mtmt.hu/api/publication/32819310},
author = {Naszódi, Márton and Venzin, Moritz},
doi = {10.1007/s00454-022-00392-x},
journal-iso = {DISCRETE COMPUT GEOM},
journal = {DISCRETE AND COMPUTATIONAL GEOMETRY},
volume = {67},
unique-id = {32819310},
issn = {0179-5376},
year = {2022},
eissn = {1432-0444},
pages = {1191-1210},
orcid-numbers = {Naszódi, Márton/0000-0002-4194-0205}
}
@conference{MTMT:33113447,
title = {Funckionális Helly-típusú tételek és gömbpoliéderek},
url = {https://m2.mtmt.hu/api/publication/33113447},
author = {Naszódi, Márton},
booktitle = {Eötvös Loránd Tudományegyetem Intézményi ÚNKP Konferencia 2022. augusztus 31.},
unique-id = {33113447},
year = {2022},
pages = {300},
orcid-numbers = {Naszódi, Márton/0000-0002-4194-0205}
}
@article{MTMT:33258982,
title = {CONTACTS IN TOTALLY SEPARABLE PACKINGS IN THE PLANE AND IN HIGH DIMENSIONS},
url = {https://m2.mtmt.hu/api/publication/33258982},
author = {Naszódi, Márton and Swanepoel, Konrad J},
doi = {10.20382/jocg.v13i1a17},
journal-iso = {J COMPUT GEOM},
journal = {JOURNAL OF COMPUTATIONAL GEOMETRY},
volume = {13},
unique-id = {33258982},
issn = {1920-180X},
year = {2022},
eissn = {1920-180X},
pages = {471-483},
orcid-numbers = {Naszódi, Márton/0000-0002-4194-0205}
}
@article{MTMT:36882730,
title = {The Honeycomb Conjecture in Normed Planes and an Alpha-Convex Variant of a Theorem of Dowker},
url = {https://m2.mtmt.hu/api/publication/36882730},
author = {Lángi, Zsolt and Wang, Shanshan},
doi = {10.1093/imrn/rnaf372},
journal-iso = {INT MATH RES NOTICES},
journal = {INTERNATIONAL MATHEMATICS RESEARCH NOTICES},
volume = {2026},
unique-id = {36882730},
issn = {1073-7928},
abstract = {The Honeycomb Conjecture states that among tilings with unit area cells in the Euclidean plane, the average perimeter of a cell is minimal for a regular hexagonal tiling. This conjecture was proved by L. Fejes Tóth for convex tilings, and by Hales for not necessarily convex tilings. In this paper we investigate the same question for tilings of a given normed plane, and show that among normal, convex tilings in a normed plane, the average squared perimeter of a cell is minimal for a tiling whose cells are translates of a centrally symmetric hexagon. We also show that the question whether the same statement is true for the average perimeter of a cell is closely related to an -convex variant of a theorem of Dowker on the area of polygons circumscribed about a convex disk. Exploring this connection we find families of norms in which the average perimeter of a cell of a tiling is minimal for a hexagonal tiling, and prove some additional related results. Finally, we apply our method to give a partial answer to a problem of Steinhaus about the isoperimetric ratios of cells of certain tilings in the Euclidean plane, appeared in an open problem book of Croft, Falconer, and Guy.},
year = {2026},
eissn = {1687-0247},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:35217849,
title = {On optimal λ-separable packings in the plane},
url = {https://m2.mtmt.hu/api/publication/35217849},
author = {Bezdek, Károly and Lángi, Zsolt},
doi = {10.26493/1855-3974.3130.d46},
journal-iso = {ARS MATH CONTEMPOR},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {25},
unique-id = {35217849},
issn = {1855-3966},
abstract = {Let P be a packing of circular disks of radius rho > 0 in the Euclidean, spherical, or hyperbolic plane. Let 0 <= A <= rho. We say that P is a A-separable packing of circular disks of radius rho if the family P ' of disks concentric to the disks of P having radius A form a totally separable packing, i.e., any two disks of P ' can be separated by a line which is disjoint from the interior of every disk of F '. This notion bridges packings of circular disks of radius rho (with A = 0) and totally separable packings of circular disks of radius rho (with A = rho). In this note we extend several theorems on the density, tightness, and contact numbers of disk packings and totally separable disk packings to A-separable packings of circular disks of radius rho in the Euclidean, spherical, and hyperbolic plane. In particular, our upper bounds (resp., lower bounds) for the density (resp., tightness) of A-separable packings of unit disks in the Euclidean plane are sharp for all 0 <= A <= 1 with the extremal values achieved by A-separable lattice packings of unit disks. On the other hand, the bounds of similar results in the spherical and hyperbolic planes are not sharp for all 0 <= A <= rho although they do not seem to be far from the relevant optimal bounds either. The proofs use local analytic and elementary geometry and are based on the so-called refined Molnar decomposition, which is obtained from the underlying Delaunay decomposition and as such might be of independent interest.},
year = {2025},
eissn = {1855-3974},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:36882825,
title = {Density bounds for unit ball packings relative to their outer parallel domains},
url = {https://m2.mtmt.hu/api/publication/36882825},
author = {Károly, Bezdek and Lángi, Zsolt},
journal-iso = {PURE AND APPLIED FUNCTIONAL ANALYSIS},
journal = {PURE AND APPLIED FUNCTIONAL ANALYSIS},
volume = {10},
unique-id = {36882825},
issn = {2189-3756},
year = {2025},
eissn = {2189-3764},
pages = {1193-1205},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:35492943,
title = {Corrigendum to “An algorithm to find maximum area polygons circumscribed about a convex polygon” [Discrete Appl. Math. 255 (2019) 98–108]},
url = {https://m2.mtmt.hu/api/publication/35492943},
author = {Ausserhofer, Markus and Dann, Susanna and Lángi, Zsolt and Tóth, Géza},
doi = {10.1016/j.dam.2024.04.013},
journal-iso = {DISCRETE APPL MATH},
journal = {DISCRETE APPLIED MATHEMATICS},
volume = {353},
unique-id = {35492943},
issn = {0166-218X},
year = {2024},
eissn = {1872-6771},
pages = {222-226},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:34069754,
title = {On monohedral tilings of a regular polygon},
url = {https://m2.mtmt.hu/api/publication/34069754},
author = {Basit, Bushra and Lángi, Zsolt},
doi = {10.1007/s00010-023-00973-y},
journal-iso = {AEQUATIONES MATH},
journal = {AEQUATIONES MATHEMATICAE},
volume = {98},
unique-id = {34069754},
issn = {0001-9054},
abstract = {A tiling of a topological disc by topological discs is called monohedral if all tiles are congruent. Maltby (J Comb Theory Ser A 66:40-52, 1994) characterized the monohedral tilings of a square by three topological discs. Kurusa et al. (Mediterr J Math 17:156, 2020) characterized the monohedral tilings of a circular disc by three topological discs. The aim of this note is to connect these two results by characterizing the monohedral tilings of any regular n-gon with at most three tiles for any n = 5.},
year = {2024},
eissn = {1420-8903},
pages = {535-555},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:34792456,
title = {Dowker-type theorems for disk-polygons in normed planes},
url = {https://m2.mtmt.hu/api/publication/34792456},
author = {Basit, Bushra and Lángi, Zsolt},
doi = {10.1016/j.disc.2024.114019},
journal-iso = {DISCRETE MATH},
journal = {DISCRETE MATHEMATICS},
volume = {347},
unique-id = {34792456},
issn = {0012-365X},
year = {2024},
eissn = {1872-681X},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:34795002,
title = {On a Dowker-Type Problem for Convex Disks with Almost Constant Curvature},
url = {https://m2.mtmt.hu/api/publication/34795002},
author = {Basit, Bushra and Lángi, Zsolt},
doi = {10.1556/012.2024.04306},
journal-iso = {STUD SCI MATH HUNG},
journal = {STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA},
volume = {61},
unique-id = {34795002},
issn = {0081-6906},
abstract = {A classical result of Dowker (Bull. Amer. Math. Soc. 50: 120-122, 1944) states that for any plane convex body 𝐾, the areas of the maximum (resp. minimum) area convex 𝑛-gons inscribed (resp. circumscribed) in 𝐾 is a concave (resp. convex) sequence. It is known that this theorem remains true if we replace area by perimeter, or convex 𝑛-gons by disk-𝑛-gons, obtained as the intersection of 𝑛 closed Euclidean unit disks. It has been proved recently that if 𝐶 is the unit disk of a normed plane, then the same properties hold for the area of 𝐶-𝑛-gons circumscribed about a 𝐶-convex disk 𝐾 and for the perimeters of 𝐶-𝑛-gons inscribed or circumscribed about a 𝐶-convex disk 𝐾, but for a typical origin-symmetric convex disk 𝐶 with respect to Hausdorff distance, there is a 𝐶-convex disk 𝐾 such that the sequence of the areas of the maximum area 𝐶-𝑛-gons inscribed in 𝐾 is not concave. The aim of this paper is to investigate this question if we replace the topology induced by Hausdorff distance with a topology induced by the surface area measure of the boundary of 𝐶.},
keywords = {AREA; Hausdorff distance; Dowker's theorems; inscribed polygon},
year = {2024},
eissn = {1588-2896},
pages = {59-72},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:34006049,
title = {From the Separable Tammes Problem to Extremal Distributions of Great Circles in the Unit Sphere},
url = {https://m2.mtmt.hu/api/publication/34006049},
author = {Bezdek, Károly and Lángi, Zsolt},
doi = {10.1007/s00454-023-00509-w},
journal-iso = {DISCRETE COMPUT GEOM},
journal = {DISCRETE AND COMPUTATIONAL GEOMETRY},
volume = {72},
unique-id = {34006049},
issn = {0179-5376},
abstract = {A family of spherical caps of the 2-dimensional unit sphere S-2 is called a totally separable packing in short, a TS-packing if any two spherical caps can be separated by a great circle which is disjoint from the interior of each spherical cap in the packing. The separable Tammes problem asks for the largest density of given number of congruent spherical caps forming a TS-packing in S-2. We solve this problem up to eight spherical caps and upper bound the density of any TS-packing of congruent spherical caps in terms of their angular radius. Based on this, we show that the centered separable kissing number of unit balls in Euclidean 3-space is 8. Furthermore, we prove bounds for the maximum of the smallest inradius of the cells of the tilings generated by n > 1 great circles in S-2. Next, we prove dual bounds for TS-coverings of S-2 by congruent spherical caps. Here a covering of S-2 by spherical caps is called a totally separable covering in short, a TS-covering if there exists a tiling generated by finitely many great circles of S-2 such that the cells of the tiling are covered by pairwise distinct spherical caps of the covering. Finally, we extend some of our bounds on TS-coverings to spherical spaces of dimension > 2.},
year = {2024},
eissn = {1432-0444},
pages = {269-309},
orcid-numbers = {Bezdek, Károly/0000-0003-3097-0430; Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:35457299,
title = {Remarks on Soft Ball Packings in Dimensions 2 and 3},
url = {https://m2.mtmt.hu/api/publication/35457299},
author = {Bezdek, Károly and Lángi, Zsolt},
doi = {10.1556/012.2024.04318},
journal-iso = {STUD SCI MATH HUNG},
journal = {STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA},
volume = {61},
unique-id = {35457299},
issn = {0081-6906},
abstract = {We study translative arrangements of centrally symmetric convex domains in the plane (resp., of congruent balls in the Euclidean 3-space) that neither pack nor cover. We define their soft density depending on a soft parameter and prove that the largest soft density for soft translative packings of a centrally symmetric convex domain with 3-fold rotational symmetry and given soft parameter is obtained for a proper soft lattice packing. Furthermore, we show that among the soft lattice packings of congruent soft balls with given soft parameter the soft density is locally maximal for the corresponding face centered cubic (FCC) lattice.},
year = {2024},
eissn = {1588-2896},
pages = {251-261},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:34550819,
title = {Morse–Smale complexes on convex polyhedra},
url = {https://m2.mtmt.hu/api/publication/34550819},
author = {Ludmány, Balázs and Lángi, Zsolt and Domokos, Gábor},
doi = {10.1007/s10998-024-00583-4},
journal-iso = {PERIOD MATH HUNG},
journal = {PERIODICA MATHEMATICA HUNGARICA},
volume = {89},
unique-id = {34550819},
issn = {0031-5303},
abstract = {Motivated by applications in geomorphology, the aim of this paper is to extend Morse–Smale theory from smooth functions to the radial distance function (measured from an internal point), defining a convex polyhedron in 3-dimensional Euclidean space. The resulting polyhedral Morse–Smale complex may be regarded, on one hand, as a generalization of the Morse–Smale complex of the smooth radial distance function defining a smooth, convex body, on the other hand, it could be also regarded as a generalization of the Morse–Smale complex of the piecewise linear parallel distance function (measured from a plane), defining a polyhedral surface. Beyond similarities, our paper also highlights the marked differences between these three problems and it also relates our theory to other methods. Our work includes the design, implementation and testing of an explicit algorithm computing the Morse–Smale complex on a convex polyhedron.},
year = {2024},
eissn = {1588-2829},
pages = {1-22},
orcid-numbers = {Ludmány, Balázs/0000-0001-5373-7610; Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:33742876,
title = {A characterization of the symmetry groups of mono-monostatic convex bodies},
url = {https://m2.mtmt.hu/api/publication/33742876},
author = {Domokos, Gábor and Lángi, Zsolt and Várkonyi, Péter László},
doi = {10.1007/s00605-023-01847-w},
journal-iso = {MONATSH MATH},
journal = {MONATSHEFTE FUR MATHEMATIK},
volume = {201},
unique-id = {33742876},
issn = {0026-9255},
abstract = {Answering a question of Conway and Guy (SIAM Rev. 11:78-82, 1969), Langi (Bull. Lond. Math. Soc. 54: 501-516, 2022) proved the existence of a monostable polyhedron with n-fold rotational symmetry for any n = 3, and arbitrarily close to a Euclidean ball. In this paper we strengthen this result by characterizing the possible symmetry groups of all mono-monostatic smooth convex bodies and convex polyhedra. Our result also answers a stronger version of the question of Conway and Guy, asked in the above paper of Langi.},
year = {2023},
eissn = {1436-5081},
pages = {703-724},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:33734944,
title = {Isoperimetric problems for zonotopes},
url = {https://m2.mtmt.hu/api/publication/33734944},
author = {Joós, Antal and Lángi, Zsolt},
doi = {10.1112/mtk.12191},
journal-iso = {MATHEMATIKA},
journal = {MATHEMATIKA},
volume = {69},
unique-id = {33734944},
issn = {0025-5793},
abstract = {Shephard (Canad. J. Math. 26 (1974), 302-321) proved a decomposition theorem for zonotopes yielding a simple formula for their volume. In this note, we prove a generalization of this theorem yielding similar formulae for their intrinsic volumes. We use this result to investigate geometric extremum problems for zonotopes generated by a given number of segments. In particular, we solve isoperimetric problems for d-dimensional zonotopes generated by d or d+1$d+1$ segments, and give asymptotic estimates for the solutions of similar problems for zonotopes generated by sufficiently many segments. In addition, we present applications of our results to the l(1) polarization problem on the unit sphere and to a vector-valued Maclaurin inequality conjectured by Brazitikos and McIntyre in 2021.},
keywords = {APPROXIMATION; VOLUMES; POINTS; intrinsic volume; Zonotope; Isoperimetric problem; Mathematics, Applied; parallelotope; ball; rhombic dodecahedron; ZONOIDS},
year = {2023},
eissn = {2041-7942},
pages = {508-534},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:32669283,
title = {On generalized Minkowski arrangements},
url = {https://m2.mtmt.hu/api/publication/32669283},
author = {Kadlicskó, Máté and Lángi, Zsolt},
doi = {10.26493/1855-3974.2550.d96},
journal-iso = {ARS MATH CONTEMPOR},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {23},
unique-id = {32669283},
issn = {1855-3966},
abstract = {The concept of a Minkowski arrangement was introduced by Fejes Tóth in 1965 as a family of centrally symmetric convex bodies with the property that no member of the family contains the center of any other member in its interior. This notion was generalized by Fejes Tóth in 1967, who called a family of centrally symmetric convex bodies a generalized Minkowski arrangement of order μ for some 0 < μ < 1 if no member K of the family overlaps the homothetic copy of any other member K′ with ratio μ and with the same center as K′. In this note we prove a sharp upper bound on the total area of the elements of a generalized Minkowski arrangement of order μ of finitely many circular disks in the Euclidean plane. This result is a common generalization of a similar result of Fejes Tóth for Minkowski arrangements of circular disks, and a result of Böröczky and Szabó about the maximum density of a generalized Minkowski arrangement of circular disks in the plane. In addition, we give a sharp upper bound on the density of a generalized Minkowski arrangement of homothetic copies of a centrally symmetric convex body.},
year = {2023},
eissn = {1855-3974},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:33561914,
title = {Discrete isoperimetric problems in spaces of constant curvature},
url = {https://m2.mtmt.hu/api/publication/33561914},
author = {Basit, Bushra and Lángi, Zsolt},
doi = {10.1112/mtk.12175},
journal-iso = {MATHEMATIKA},
journal = {MATHEMATIKA},
volume = {69},
unique-id = {33561914},
issn = {0025-5793},
abstract = {The aim of this paper is to prove isoperimetric inequalities for simplices and polytopes with d+2$d+2$ vertices in Euclidean, spherical and hyperbolic d-space. In particular, we find the minimal volume d-dimensional hyperbolic simplices and spherical tetrahedra of a given inradius. Furthermore, we investigate the properties of maximal volume spherical and hyperbolic polytopes with d+2$d+2$ vertices with a given circumradius, and the hyperbolic polytopes with d+2$d+2$ vertices with a given inradius and having a minimal volume or minimal total edge length. Finally, for any 1 <= k <= d$1 \leqslant k \leqslant d$, we investigate the properties of Euclidean simplices and polytopes with d+2$d+2$ vertices having a fixed inradius and a minimal volume of its k-skeleton. The main tool of our investigation is Euclidean, spherical and hyperbolic Steiner symmetrization.},
year = {2022},
eissn = {2041-7942},
pages = {33-50},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:32517495,
title = {On k-diametral point configurations in Minkowski spaces},
url = {https://m2.mtmt.hu/api/publication/32517495},
author = {Bezdek, Károly and Lángi, Zsolt},
doi = {10.1016/j.disc.2021.112700},
journal-iso = {DISCRETE MATH},
journal = {DISCRETE MATHEMATICS},
volume = {345},
unique-id = {32517495},
issn = {0012-365X},
abstract = {The structure of k-diametral point configurations in Minkowski d-space is shown to be closely related to the properties of k-antipodal point configurations in Rd. In particular, the maximum size of k-diametral point configurations of Minkowski d-spaces is obtained for given k >= 2 and d >= 2 generalizing Petty's results (Petty, 1971 [24]) on equilateral sets in Minkowski spaces. Furthermore, bounds are derived for the maximum size of k-diametral point configurations in given Minkowski d-space (resp., Euclidean d-space). Some of these results have analogues for point sets, which are discussed as well. In the proofs convexity methods are combined with volumetric estimates and combinatorial properties of diameter graphs. (C) 2021 Elsevier B.V. All rights reserved.},
year = {2022},
eissn = {1872-681X},
orcid-numbers = {Bezdek, Károly/0000-0003-3097-0430; Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:30548681,
title = {Tracking Critical Points on Evolving Curves and Surfaces},
url = {https://m2.mtmt.hu/api/publication/30548681},
author = {Domokos, Gábor and Lángi, Zsolt and Sipos, András Árpád},
doi = {10.1080/10586458.2018.1556136},
journal-iso = {EXP MATH},
journal = {EXPERIMENTAL MATHEMATICS},
volume = {31},
unique-id = {30548681},
issn = {1058-6458},
abstract = {In recent years it became apparent that geophysical abrasion can be well characterized by the time evolution N(t) of the number N of static balance points of the abrading particle. Static balance points correspond to the critical points of the particle's surface represented as a scalar distance function r, measured from the center of mass of the particle, so their time evolution can be expressed as N (r (t)) . The mathematical model of the particle can be constructed on two scales: on the macro (global) scale the particle may be viewed as a smooth, convex manifold described by the smooth distance function r with N = N (r) equilibria, while on the micro (local) scale the particle's natural model is a finely discretized, convex polyhedral approximation r(Delta) of r, with N-Delta = N(r(Delta)) equilibria. There is strong intuitive evidence suggesting that under some particular evolution models (e.g., curvature-driven flows) N(t) and N (Delta)(t) primarily evolve in the opposite manner (i.e. if one is increasing then the other is decreasing and vice versa). This observation appears to be a key factor in tracking geophysical abrasion. Here we create the mathematical framework necessary to understand these phenomena more broadly, regardless of the particular evolution equation. We study micro and macro events in one-parameter families of curves and surfaces, corresponding to bifurcations triggering the jumps in N(t) and N (Delta)(t). Based on this analysis we show that the intuitive picture developed for curvature-driven flows is not only correct, it has universal validity, as long as the evolving surface r is smooth. In this case, bifurcations associated with r and r (Delta) are coupled to some extent: resonance-like phenomena in N (Delta)(t) can be used to forecast downward jumps in N(t) (but not upward jumps). Beyond proving rigorous results in the case of evolving planar curves for the Delta -> 0 limit on the nontrivial interplay between singularities in the discrete and continuum approximations we also show that our mathematical model is structurally stable. This property serves as the basis for the second, experimental part of our research where we demonstrate via computer simulations that the phenomena on evolving surfaces appear to be closely analogous to the planar case, however, they also show additional geometric features which are still not completely understood.},
year = {2022},
eissn = {1944-950X},
pages = {1-20},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343; Sipos, András Árpád/0000-0003-0440-2165}
}
@article{MTMT:30799093,
title = {Plato’s Error and a Mean Field Formula for Convex Mosaics},
url = {https://m2.mtmt.hu/api/publication/30799093},
author = {Domokos, Gábor and Lángi, Zsolt},
doi = {10.1007/s10516-019-09455-w},
journal-iso = {AXIOMATHES},
journal = {AXIOMATHES},
volume = {32},
unique-id = {30799093},
issn = {1122-1151},
abstract = {Plato claimed that the regular solids are the building blocks of all matter. His views, commonly referred to as the geometric atomistic model, had enormous impact on human thought despite the fact that four of the five Platonic solids can not fill space without gaps. In this paper we quantify these gaps, showing that the errors in Plato’s estimates were quite small. We also develop a mean field approximation to convex honeycombs using a generalized version of Plato’s idea. This approximation not only admits to view convex mosaics in d=3 dimensions as a continuum but we also find that it is quite accurate, showing that Plato’s geometric intuition may have been remarkable.},
year = {2022},
eissn = {1572-8390},
pages = {889-905},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:31009246,
title = {On Some Average Properties of Convex Mosaics},
url = {https://m2.mtmt.hu/api/publication/31009246},
author = {Domokos, Gábor and Lángi, Zsolt},
doi = {10.1080/10586458.2019.1691090},
journal-iso = {EXP MATH},
journal = {EXPERIMENTAL MATHEMATICS},
volume = {31},
unique-id = {31009246},
issn = {1058-6458},
abstract = {In a convex mosaic in we denote the average number of vertices of a cell by and the average number of cells meeting at a node by Except for the d = 2 planar case, there is no known formula prohibiting points in any range of the plane (except for the unphysical strips). Nevertheless, in d = 3 dimensions if we plot the 28 points corresponding to convex uniform honeycombs, the 28 points corresponding to their duals and the 3 points corresponding to Poisson-Voronoi, Poisson-Delaunay and random hyperplane mosaics, then these points appear to accumulate on a narrow strip of the plane. To explore this phenomenon we introduce the harmonic degree of a d-dimensional mosaic. We show that the observed narrow strip on the plane corresponds to a narrow range of We prove that for every there exists a convex mosaic with harmonic degree and we conjecture that there exist no d-dimensional mosaic outside this range. We also show that the harmonic degree has deeper geometric interpretations. In particular, in case of Euclidean mosaics it is related to the average of the sum of vertex angles and their polars, and in case of 2 D mosaics, it is related to the average excess angle.},
year = {2022},
eissn = {1944-950X},
pages = {783-793},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:33078387,
title = {Volume of the Minkowski sums of star-shaped sets},
url = {https://m2.mtmt.hu/api/publication/33078387},
author = {Fradelizi, Matthieu and Lángi, Zsolt and Zvavitch, Artem},
doi = {10.1090/bproc/97},
journal-iso = {PROC AM MATH SOC SER B},
journal = {PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY SERIES B},
volume = {9},
unique-id = {33078387},
abstract = {For a compact set A ⊂ R d A \subset \mathbb {R}^d and an integer k ≥ 1 k\ge 1 , let us denote by A [ k ] = { a 1 + ⋯ + a k : a 1 , … , a k ∈ A } = ∑ i = 1 k A \begin{equation*} A[k] = \left \{a_1+\cdots +a_k: a_1, \ldots , a_k\in A\right \}=\sum _{i=1}^k A \end{equation*} the Minkowski sum of k k copies of A A . A theorem of Shapley, Folkmann and Starr (1969) states that 1 k A [ k ] \frac {1}{k}A[k] converges to the convex hull of A A in Hausdorff distance as k k tends to infinity. Bobkov, Madiman and Wang [ Concentration, functional inequalities and isoperimetry , Amer. Math. Soc., Providence, RI, 2011] conjectured that the volume of 1 k A [ k ] \frac {1}{k}A[k] is nondecreasing in k k , or in other words, in terms of the volume deficit between the convex hull of A A and 1 k A [ k ] \frac {1}{k}A[k] , this convergence is monotone. It was proved by Fradelizi, Madiman, Marsiglietti and Zvavitch [C. R. Math. Acad. Sci. Paris 354 (2016), pp. 185–189] that this conjecture holds true if d = 1 d=1 but fails for any d ≥ 12 d \geq 12 . In this paper we show that the conjecture is true for any star-shaped set A ⊂ R d A \subset \mathbb {R}^d for d = 2 d=2 and d = 3 d=3 and also for arbitrary dimensions d ≥ 4 d \ge 4 under the condition k ≥ ( d − 1 ) ( d − 2 ) k \ge (d-1)(d-2) . In addition, we investigate the conjecture for connected sets and present a counterexample to a generalization of the conjecture to the Minkowski sum of possibly distinct sets in R d \mathbb {R}^d , for any d ≥ 7 d \geq 7 .},
year = {2022},
eissn = {2330-1511},
pages = {358-372},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:32613562,
title = {On the convex hull and homothetic convex hull functions of a convex body},
url = {https://m2.mtmt.hu/api/publication/32613562},
author = {G. Horváth, Ákos and Lángi, Zsolt},
doi = {10.1007/s10711-022-00673-y},
journal-iso = {GEOMETRIAE DEDICATA},
journal = {GEOMETRIAE DEDICATA},
volume = {216},
unique-id = {32613562},
issn = {0046-5755},
abstract = {The aim of this note is to investigate the properties of the convex hull and the homothetic convex hull functions of a convex body K in Euclidean n-space, defined as the volume of the union of K and one of its translates, and the volume of K and a translate of a homothetic copy of K, respectively, as functions of the translation vector. In particular, we prove that the convex hull function of the body K does not determine K. Furthermore, we prove the equivalence of the polar projection body problem raised by Petty, and a conjecture of G.Horváth and Lángi about translative constant volume property of convex bodies. We give a short proof of some theorems of Jerónimo-Castro about the homothetic convex hull function, and prove a homothetic variant of the translative constant volume property conjecture for 3-dimensional convex polyhedra. We also apply our results to describe the properties of the illumination bodies of convex bodies.},
year = {2022},
eissn = {1572-9168},
orcid-numbers = {G. Horváth, Ákos/0000-0003-2371-4818; Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:32541127,
title = {Extremal convex polygons inscribed in a given convex polygon},
url = {https://m2.mtmt.hu/api/publication/32541127},
author = {Ködmön, Csenge Lili and Lángi, Zsolt},
doi = {10.1016/j.comgeo.2021.101844},
journal-iso = {COMP GEOM-THEOR APPL},
journal = {COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS},
volume = {102},
unique-id = {32541127},
issn = {0925-7721},
abstract = {A convex polygon Q is inscribed in a convex polygon P if every side of P contains at least one vertex of Q. We present algorithms for finding a minimum area and a minimum perimeter convex polygon inscribed in any given convex n-gon in O(n) and O(n(3)) time, respectively. We also investigate other variants of this problem.},
year = {2022},
eissn = {1879-081X},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:32729942,
title = {An isoperimetric problem for three-dimensional parallelohedra},
url = {https://m2.mtmt.hu/api/publication/32729942},
author = {Lángi, Zsolt},
doi = {10.2140/pjm.2022.316.169},
journal-iso = {PAC J MATH},
journal = {PACIFIC JOURNAL OF MATHEMATICS},
volume = {316},
unique-id = {32729942},
issn = {0030-8730},
abstract = {The aim of this note is to investigate isoperimetric-type problems for 3-dimensional parallelohedra; that is, for convex polyhedra whose translates tile the 3-dimensional Euclidean space. Our main result states that among 3-dimensional parallelohedra with unit volume, the one with minimal mean width is the regular truncated octahedron.},
year = {2022},
eissn = {1945-5844},
pages = {169-181},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:32749811,
title = {A solution to some problems of Conway and Guy on monostable polyhedra},
url = {https://m2.mtmt.hu/api/publication/32749811},
author = {Lángi, Zsolt},
doi = {10.1112/blms.12579},
journal-iso = {B LOND MATH SOC},
journal = {BULLETIN OF THE LONDON MATHEMATICAL SOCIETY},
volume = {54},
unique-id = {32749811},
issn = {0024-6093},
abstract = {A convex polyhedron is called monostable if it can rest in stable position only on one of its faces. The aim of this paper is to investigate three questions of Conway, regarding monostable polyhedra, which first appeared in a 1969 paper of Goldberg and Guy. In this note, we answer two of these problems and make a conjecture about the third one. The main tool of our proof is a general theorem describing approximations of smooth convex bodies by convex polyhedra in terms of their static equilibrium points. As another application of this theorem, we prove the existence of a convex polyhedron with only one stable and one unstable point.},
keywords = {EQUILIBRIA; BODIES; EVERY POINT},
year = {2022},
eissn = {1469-2120},
pages = {501-516},
orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343}
}
@article{MTMT:36281398,
title = {Estimates on the decay of the Laplace–Pólya integral},
url = {https://m2.mtmt.hu/api/publication/36281398},
author = {Ambrus, Gergely and Gárgyán, Barnabás},
doi = {10.1112/blms.70157},
journal-iso = {B LOND MATH SOC},
journal = {BULLETIN OF THE LONDON MATHEMATICAL SOCIETY},
volume = {57},
unique-id = {36281398},
issn = {0024-6093},
abstract = {The Laplace–Pólya integral, defined by , appears in several areas of mathematics. We study this quantity by combinatorial methods; accordingly, our investigation focuses on the values at integer . Our main result establishes a lower bound for the ratio which extends and generalises the previous estimates of Lesieur and Nicolas [23], and provides a natural counterpart to the upper estimate established in our previous work [2]. We derive the statement by purely combinatorial, elementary arguments. As a corollary, we deduce that no subdiagonal central sections of the unit cube are extremal, apart from the minimal, maximal, and the main diagonal sections. We also prove several consequences for Eulerian numbers.},
year = {2025},
eissn = {1469-2120},
pages = {3360-3379},
orcid-numbers = {Ambrus, Gergely/0000-0003-1246-6601}
}
@article{MTMT:36437865,
title = {Covering Spiky Annuli by Planks},
url = {https://m2.mtmt.hu/api/publication/36437865},
author = {Ambrus, Gergely and Huddell, Julian and Lai, Maggie and Quirk, Matthew and Williams, Elias},
doi = {10.1007/s00454-025-00799-2},
journal-iso = {DISCRETE COMPUT GEOM},
journal = {DISCRETE AND COMPUTATIONAL GEOMETRY},
unique-id = {36437865},
issn = {0179-5376},
year = {2025},
eissn = {1432-0444},
orcid-numbers = {Ambrus, Gergely/0000-0003-1246-6601}
}
@article{MTMT:33834838,
title = {The density of planar sets avoiding unit distances},
url = {https://m2.mtmt.hu/api/publication/33834838},
isbn = {9788131203767},
author = {Ambrus, Gergely and Csiszárik, Adrián and Matolcsi, Máté and Varga, Dániel and Zsámboki, Pál},
doi = {10.1007/s10107-023-02012-9},
journal-iso = {MATH PROGRAM},
journal = {MATHEMATICAL PROGRAMMING},
volume = {207},
unique-id = {33834838},
issn = {0025-5610},
abstract = {By improving upon previous estimates on a problem posed by L. Moser, we prove a conjecture of Erdős that the density of any measurable planar set avoiding unit distances is less than 1/4. Our argument implies the upper bound of 0.2470.},
year = {2024},
eissn = {1436-4646},
pages = {303-327},
orcid-numbers = {Ambrus, Gergely/0000-0003-1246-6601; Matolcsi, Máté/0000-0003-4889-697X}
}
@article{MTMT:34675004,
title = {Non-diagonal critical central sections of the cube},
url = {https://m2.mtmt.hu/api/publication/34675004},
author = {Ambrus, Gergely and Gárgyán, Barnabás},
doi = {10.1016/j.aim.2024.109524},
journal-iso = {ADV MATH},
journal = {ADVANCES IN MATHEMATICS},
volume = {441},
unique-id = {34675004},
issn = {0001-8708},
year = {2024},
eissn = {1090-2082},
orcid-numbers = {Ambrus, Gergely/0000-0003-1246-6601}
}
@article{MTMT:35186951,
title = {Colorful vector balancing},
url = {https://m2.mtmt.hu/api/publication/35186951},
author = {Ambrus, Gergely and Heck, Rainie},
doi = {10.1112/mtk.12274},
journal-iso = {MATHEMATIKA},
journal = {MATHEMATIKA},
volume = {70},
unique-id = {35186951},
issn = {0025-5793},
abstract = {We extend classical estimates for the vector balancing constant of equipped with the Euclidean and the maximum norms proved in the 1980s by showing that for and , given vector families with , one may select vectors with for , and for . These bounds are sharp and asymptotically sharp, respectively, for . The proofs combine linear algebraic and probabilistic methods with a Gaussian random walk argument.},
year = {2024},
eissn = {2041-7942},
orcid-numbers = {Ambrus, Gergely/0000-0003-1246-6601}
}
@article{MTMT:34541690,
title = {Az Erdős–Moser sejtés bizonyítása},
url = {https://m2.mtmt.hu/api/publication/34541690},
author = {Ambrus, Gergely and Varga, Dániel},
journal-iso = {ÉRINTŐ},
journal = {ÉRINTŐ : ELEKTRONIKUS MATEMATIKAI LAPOK},
unique-id = {34541690},
year = {2023},
eissn = {2559-9275},
orcid-numbers = {Ambrus, Gergely/0000-0003-1246-6601}
}
@article{MTMT:32510846,
title = {Piercing the chessboard},
url = {https://m2.mtmt.hu/api/publication/32510846},
author = {Ambrus, Gergely and Bárány, Imre and Frankl, Péter and Varga, Dániel},
doi = {10.1137/21M146048X},
journal-iso = {SIAM J DISCRETE MATH},
journal = {SIAM JOURNAL ON DISCRETE MATHEMATICS},
volume = {37},
unique-id = {32510846},
issn = {0895-4801},
year = {2023},
eissn = {1095-7146},
pages = {1457-1471},
orcid-numbers = {Ambrus, Gergely/0000-0003-1246-6601}
}
@article{MTMT:32617382,
title = {A generalization of Bang's lemma},
url = {https://m2.mtmt.hu/api/publication/32617382},
author = {Ambrus, Gergely},
doi = {10.1090/proc/16228},
journal-iso = {P AM MATH SOC},
journal = {PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY},
volume = {151},
unique-id = {32617382},
issn = {0002-9939},
abstract = {We prove a common extension of Bang’s and Kadets’ lemmas for contact pairs, in the spirit of the Colourful Carathéodory Theorem. We also formulate a generalized version of the affine plank problem and prove it under special assumptions. In particular, we obtain a generalization of Kadets’ theorem. Finally, we give applications to problems regarding translative and homothetic coverings.},
year = {2023},
eissn = {1088-6826},
pages = {1277-1284},
orcid-numbers = {Ambrus, Gergely/0000-0003-1246-6601}
}
@article{MTMT:32257228,
title = {Quantitative Helly-type theorems via sparse approximation},
url = {https://m2.mtmt.hu/api/publication/32257228},
author = {Hugo Almendra-Hernández, Víctor and Ambrus, Gergely and Kendall, Matthew},
doi = {10.1007/s00454-022-00441-5},
journal-iso = {DISCRETE COMPUT GEOM},
journal = {DISCRETE AND COMPUTATIONAL GEOMETRY},
volume = {70},
unique-id = {32257228},
issn = {0179-5376},
abstract = {We prove the following sparse approximation result for polytopes. Assume that Q is a polytope in John's position. Then there exist at most 2d vertices of Q whose convex hull Q' satisfies Q subset of -2d(2) Q'. As a consequence, we retrieve the best bound for the quantitative Helly-type result for the volume, achieved by Brazitikos, and improve on the strongest bound for the quantitative Helly-type theorem for the diameter, shown by Ivanov and Naszodi: We prove that given a finite family F of convex bodies in R-d with intersection K, we may select at most 2d members of F such that their intersection has volume at most (cd)(3d)(/2) vol K, and it has diameter at most 2d(2) diam K, for some absolute constant c > 0.},
year = {2023},
eissn = {1432-0444},
pages = {1707-1714},
orcid-numbers = {Ambrus, Gergely/0000-0003-1246-6601}
}
@article{MTMT:31840414,
title = {Density Estimates of 1-Avoiding Sets via Higher Order Correlations},
url = {https://m2.mtmt.hu/api/publication/31840414},
author = {Ambrus, Gergely and Matolcsi, Máté},
doi = {10.1007/s00454-020-00263-3},
journal-iso = {DISCRETE COMPUT GEOM},
journal = {DISCRETE AND COMPUTATIONAL GEOMETRY},
volume = {67},
unique-id = {31840414},
issn = {0179-5376},
abstract = {We improve the best known upper bound on the density of a planar measurable set A containing no two points at unit distance to 0.25442. We use a combination of Fourier analytic and linear programming methods to obtain the result. The estimate is achieved by means of obtaining new linear constraints on the autocorrelation function of A utilizing triple-order correlations in A, a concept that has not been previously studied. © 2020, The Author(s).},
keywords = {Linear programming; Harmonic analysis; Distance-avoiding sets; Chromatic number of the plane},
year = {2022},
eissn = {1432-0444},
pages = {1245-1256},
orcid-numbers = {Ambrus, Gergely/0000-0003-1246-6601; Matolcsi, Máté/0000-0003-4889-697X}
}
@misc{MTMT:31874254,
title = {Longest k-monotone chains},
url = {https://m2.mtmt.hu/api/publication/31874254},
author = {Ambrus, Gergely},
unique-id = {31874254},
year = {2022},
pages = {&},
orcid-numbers = {Ambrus, Gergely/0000-0003-1246-6601}
}
@article{MTMT:32257262,
title = {Critical central sections of the cube},
url = {https://m2.mtmt.hu/api/publication/32257262},
author = {Ambrus, Gergely},
doi = {10.1090/proc/15955},
journal-iso = {P AM MATH SOC},
journal = {PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY},
volume = {150},
unique-id = {32257262},
issn = {0002-9939},
year = {2022},
eissn = {1088-6826},
pages = {4463-4474},
orcid-numbers = {Ambrus, Gergely/0000-0003-1246-6601}
}
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