István Tomon: Dedekind's problem in the hypergrid

Abstract: Dedekind's problem from 1897 is one of the oldest problems in enumerative combinatorics. It simply asks for the number of monotone Boolean functions on n variables, or equivalently, the number of antichains in the Boolean lattice 2^[n]. There is no known formula for this problem, and the asymptotic growth rate was only found in the 70's by Kleitman and Markowsky. I will talk about the natural generalization of this problem, in which one is interested in the number of antichains of the hypergrid [t]^n. This problem received a lot of attention in the past two decades due to surprising connections to Ramsey theory. Based on joint work with Victor Falgas-Ravry and Eero Räty.