2021/03/09 by Sami Assaf, Assaf, Sami H.
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2103.05207
openalex publication_date 2021/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new paradigm for proving the Schur P-positivity. 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 generalization with a new application to the product of Schur P-functions.