2025/26 tavasz
Extremal Set Sytems
Thursday, 10:30 - 12:00, Déli tömb 1-110
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: Erdős 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
April 23: random version of Sperner's theorem
April 30: forbidden subposet problem, chain-partition method, an example for D3
May 14: Daisy conjecture, the counterxample of Ellis, Ivan, and Leader (proofs in previous note)