2025/26 tavasz

Extremal Set Sytems

Thursday, 10:30 - 12:00, Déli tömb 1-110

Topics:
Sperner type theorems: Sperner, Erdõs, LYM, kLYM, Bollobás inequalities, Dilworth, Mirsky, symmetric chain decomposition
Shadow theorem: full version and Lovász version
Intersection theorems: Erdõs-Ko-Rado (several proofs), Hilton-Milner and other covering number results, number of intersecting families, non-uniform theorems, L-intersecting families
Combining intersection and Sperner: t-intersecting k-Sperner families
Sunflowers
Erdõs Matching Conjecture
Forbidden subposet problem: weak, strong, saturation


Notes:
February 10: antichain, k-Sperner, LYM, kLYM, Mirsky, symmetric chain decomposition (Dilworth proof in notes, but presented next time)
February 18: Dilworth, Bollobás inequality, Sauer-Shelah
February 25: shadow theorem (proof from Dömötör), EKR from shadow theorem
March 5: shadow: Lovász version (proof in Feb 18 class's notes), EKR cycle proof
March 12: isoperimetry in hypercube, EKR polynomial method proof
March 19: Hilton-Milner theorem
March 26: non-uniform t-intersecting families (Katona, proof in notes of previous class), Ahlswede-Khatchatrian (without proof), shadow theorem for intersecting families
April 9: Erdõs matching conjecture, Frankl's theorem. Milner's theorem on intersecting Sperner families.
April 16: k-unif intersecting families with covering number k, number of (maximal) intersecting families