Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials

2020/04/24 by Sylvie Corteel, J. Haglund, Corteel, Sylvie +7 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2004.11907

openalex publication_date 2020/04/24 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We present several new and compact formulas for the modified and integral form of the Macdonald polynomials, building on the compact "multiline queue" formula for Macdonald polynomials due to Corteel, Mandelshtam, and Williams. We also introduce a new quasisymmetric analogue of Macdonald polynomials. These "quasisymmetric Macdonald polynomials" refine the (symmetric) Macdonald polynomials and specialize to the quasisymmetric Schur polynomials defined by Haglund, Luoto, Mason, and van Willigenburg.

Cited by

• New formulas for Macdonald polynomials via the multispecies exclusion and zero range processes
• The monomial expansions for modified Macdonald polynomials

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