Leírás
Abstract:
We will discuss the following problems from additive combinatorics.
1. For the largest possible size of a subset of Z_6^n avoiding 6-term arithmetic progressions we have r_6(Z_6^n)\leq 5.709^n. The current list of pairs of those k, m for which it is known whether r_k(Z_m^n) is exponentially smaller than m^n consists of (k=3, 2<m arbitrary) and (k\leq 6, 6|m arbitrary).
2. Let A be a finite, nonempty subset of an abelian group. We show that if every element of A is a sum of two other elements, then A has a nonempty zero-sum subset. That is, a (finite, nonempty) sum-full subset of an abelian group is not zero-sum-free.
The proofs are rather short, making it possible to cover both in this talk. The first result is joint work with R. Palincza, the second with V.F. Lev and J. Nagy.
For Zoom access please contact Andras Biro (biro.andras[a]renyi.hu).