Combinatorics Seminar: "Positivity Among P-Partition Generating Functions"

Abstract: Given a labeled partially ordered set (poset) P labeled by w, a (P,w)-partition is an order-preserving map from the labeled poset to the positive integers that respects certain strictness conditions imparted by the label. We can associate with labeled poset its partition enumerator, a quasisymmetric function known to be positive in Gessel's Fundamental Basis. This partition enumerator constructed from a labeled poset is a quasisymmetric analogue to skew-Schur functions constructed from skew shapes, well known to be positive in the Schur basis for symmetric functions. I will give an overview of the topic and present recent work with Peter McNamara giving some simple necessary and separate sufficient conditions that can determine when the difference of two (P,w)-partition enumerators for two distinct labeled posets is positive in the Fundamental Basis.

Host: Martha Precup