Bender–Knuth involutions for types B and C

Álvaro Gutiérrez

doi:10.37236/12571

Bender–Knuth involutions for types B and C

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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.

Original language	English
Article number	P2.59
Journal	Electronic Journal of Combinatorics
Volume	31
Issue number	2
DOIs	https://doi.org/10.37236/12571
Publication status	Published - 28 Jun 2024

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title = "Bender–Knuth involutions for types B and C",

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{\textquoteright}s classic involutions for type A.",

author = "{\'A}lvaro Guti{\'e}rrez",

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T1 - Bender–Knuth involutions for types B and C

AU - Gutiérrez, Álvaro

PY - 2024/6/28

Y1 - 2024/6/28

N2 - 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.

AB - 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.

UR - https://arxiv.org/abs/2311.10659

U2 - 10.37236/12571

DO - 10.37236/12571

M3 - Article (Academic Journal)

SN - 1077-8926

VL - 31

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

IS - 2

M1 - P2.59

ER -

Bender–Knuth involutions for types B and C

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