Algebraic and enumerative combinatorics seminar-Karen Yeats

Title:Sizes of witnesses in covtree

Abstract: Here is a purely combinatorial problem that arose in causal set theory.  Let {P_1, ... , P_k} be distinct unlabelled posets all with n elements.  Suppose there is a poset Q such that {P_1, ... , P_k} is exactly the set of downsets of Q of size n up to isomorphism. Given n and k can we give a tight upper bound on the minimum size of such a Q? As with newspaper headlines, the answer to the question is no, at least for the moment, but I'll explain what we do know.  Joint work with Jette Gutzeit, Kimia Shaban, and Stav Zalel.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm,