Queer dual equivalence graphs

Abstract

We introduce a new paradigm for proving the Schur P -positivity of a given quasi-symmetric function. Generalizing dual equivalence, we give an axiomatic definition for a family of involutions on a set of objects to be a queer dual equivalence, and we prove whenever such a family exists, the fundamental quasisymmetric generating function is Schur P -positive. In contrast with shifted dual equivalence, the queer dual equivalence involutions restrict to a dual equivalence when the queer involution is omitted. We highlight the difference between these two generalizations with a new appli-cation to the product of Schur P -functions.