Sam Hopkins: Order Polynomial Product Formulas and Poset Dynamics

Abstract

I'll present a heuristic for finding special families of partially ordered sets. The heuristic says that the posets with order polynomial product formulas are the same as the posets with good dynamical behavior. Here the order polynomial is a certain enumerative invariant of the poset. Meanwhile, the dynamics in question come from two invertible operators called promotion (acting on linear extensions) and rowmotion (acting on order ideals and P-partitions). This talk includes joint work with Tri Lai, and with Martin Rubey.