Bender-Knuth involutions for types B and C

2023/11/17 by Álvaro Gómez‐Gutiérrez, Gutiérrez, Álvaro · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Advanced Algebra and Geometry

paper · doi:10.48550/arxiv.2311.10659

Abstract

We show that the combinatorial definitions of King and Sundaram of the symmetric polynomials of types B and C are indeed symmetric, in the sense that they are invariant by the action of the Weyl groups. Our proof is combinatorial and inspired by Bender and Knuth's classic involutions for type A.

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