Frankl’s conjecture for dense families.
Ilan Karpas
Tuesday, December 18, 2018, 10:45 – 11:45, -101
Abstract:
A union closed family F is a family of sets, so that for any two sets A,B in F, A$\cup$B is also on F. Frankl conjectured in 1979 that for any union-closed family F of subsets of [n], there is some element i $\in$ [n] that appears in at least half the members of F.
| We prove that the conjecture is true if | F | >= 2^{n-1}, using tools from boolean analysis. |