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arXiv · 2503.06051

Probabilistic Entry Swapping Bijections for Non-Attacking Fillings

Guilherme Zeus Dantas e Moura·Olya Mandelshtam
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Abstract

Non-attacking fillings are combinatorial objects central to the theory of Macdonald polynomials. A probabilistic bijection for partition-shaped non-attacking fillings was introduced by Mandelshtam (2024) to prove a compact formula for symmetric Macdonald polynomials. In this work, we generalize this probabilistic bijection to composition-shaped non-attacking fillings. As an application, we provide a bijective proof to extend a symmetry theorem for permuted-basement Macdonald polynomials established by Alexandersson (2019), proving a version with fewer assumptions.

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Guilherme Zeus Dantas e Moura, Olya Mandelshtam. 2025-03-08. Probabilistic Entry Swapping Bijections for Non-Attacking Fillings. https://arxiv.org/abs/2503.06051

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