Cyclic Sieving for a Family of Semistandard Tableaux

2023/02/27 by Joshua Basman Monterrubio, Monterrubio, Joshua Basman, Graeme Henrickson +3
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2302.14143

Abstract

We give a new cyclic sieving phenomenon for semistandard Young tableaux SSYT(λ,μ) of shape λ=(m,n^b) and content μ, a (b+2)-tuple. We prove that (SSYT(λ,μ),⟨ ∂^b+2 ⟩, f(q)) exhibits the cyclic sieving phenomenon, where ∂ is the jeu de taquin promotion operator and f(q) is a modified Kostka-Foulkes polynomial \widetildeK_λ,μ(q), up to a power of q.

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