MIT-Harvard-MSR Combinatorics- Seminar

Friday, October 01, 2021 at 4:15pm to 5:15pm

77 Massachusetts Avenue, Building 2, Room 139

Speaker:  Noam Lifshitz (Hebrew Univedrsity of Jerusalem)

Title:  Forbidden intersection problems


Let F be a family of k-element subsets of {1,...,n}. F is said to be t-avoiding if no two sets in F have intersection of size exactly t.  The forbidden intersection problem of Erdős and Sós from 1975 asks how large can a t-avoiding family be (as a function of n, k and t). In the talk we solve the problem for 2t <k <0.499n and n >n_0(t) sufficiently large. 

We also solve analogue problems for the multicube {1,...,m}^n and the symmetric group S_n, provided that n is sufficiently large. 

Based on joint works with Ellis, Long, Keevash, Keller, and Minzer.

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