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arXiv · 2610.29950

Compression Formula for Nonattacking Fillings of Non-symmetric Macdonald Polynomials

Alexander P. Stewart
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Abstract

Macdonald polynomials are an important family of orthogonal polynomials that have applications to statistical physics. Corteel, Mandelshtam, and Williams proved a combinatorial model involving multiline queues for partitions; however, their work does not apply to weak compositions in general. We conjecture a first step towards this direction via a variant of the nonattacking filling model for nonsymmetric Macdonald Polynomials $E_μ$. This new model compresses the classical nonattacking filling model of Haglund, Haiman, and Loehr and mirrors the concept of trivial pairs in the multiline queue model. We prove it for a large family of weak compositions and explain the difficulty of extending this proof to the general case.

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Alexander P. Stewart. 2026-10-21. Compression Formula for Nonattacking Fillings of Non-symmetric Macdonald Polynomials. https://arxiv.org/abs/2610.29950

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