Journal of Combinatorics
Volume 14 (2023)
Queer dual equivalence graphs
Pages: 21 – 51
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 application to the product of Schur $P$‑functions.
shifted tableaux, Schur $P$-functions, Schur $Q$-functions, dual equivalence graph
2010 Mathematics Subject Classification
Primary 05E05. Secondary 05A05, 05E10.
The author’s work was supported in part by NSF grant DMS-1763336.
Received 6 May 2021
Accepted 28 September 2021
Published 19 August 2022