On the sizes of t-intersecting k-chain-free families

Description of video

Date: 10/6/22
Speaker :Patkós Balázs


    A set system F is tintersecting, if the size of the intersection of every pair of its elements has size at least t.
    A set system F is kSperner, if it does not contain a chain of length k+1.

    Our main result is the following:
    Suppose that k and t are fixed positive integers, where  n+t is even with tn and n is large enough.
    If F2[n] is a t-intersecting k-Sperner family, then |F| has size at most  the size of the sum of
    k layers, of sizes (n+t)/2,,(n+t)/2+k1.

    This bound is best possible. The case when n+t is odd remains open.

    Joint work with Józsi Balogh and Will Linz.