McCabe Olsen, University of Kentucky.

Title: Ehrhart theory and ordered set partitions

Abstract: Given a lattice polytope P, one of the central questions in Ehrhart theory is to describe the h*-polynomial (or h*-vector) of P, as this encodes and detects certain algebraic and geometric properties of P. Given that the coefficients of the h*-polynomial are nonnegative integers, it is natural (for a combinatorialist) to wishfully think that these coefficients count something; that is, ideally this polynomial encodes some statistic on some combinatorial object. In this talk, we will discuss some conjectures of Nick Early regarding the h*-polynomial of two well-known polytopes, namely dilated unit simplices and hypersimplices, involving a winding number statistic on certain decorated ordered set partitions. We will provide a proof to one of these conjectures and discuss the other.

For more details, see Discrete CATS website