Bijective proofs of some coinversion identities related to Macdonald polynomials

2022/10/20 by Nicholas A. Loehr, Loehr, Nicholas A. · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2210.11286

openalex publication_date 2022/10/20 · openalex created_date 2022/10/24 · openalex updated_date 2026/07/28

Abstract

This paper gives bijective proofs of some novel coinversion identities first discovered by Ayyer, Mandelshtam, and Martin (arxiv:2011.06117) as part of their proof of a new combinatorial formula for the modified Macdonald polynomials H_μ. Those authors used intricate algebraic manipulations of q-binomial coefficients to prove these identities, which imply the existence of certain bijections needed in their proof that their formula satisfies the axioms characterizing H_μ. They posed the open problem of constructing such bijections explicitly. We resolve that problem here.

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• New formulas for Macdonald polynomials via the multispecies exclusion and zero range processes

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