Probabilistic Entry Swapping Bijections for Non-Attacking Fillings
Combinatorics
2025-03-11 v1
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.
Cite
@article{arxiv.2503.06051,
title = {Probabilistic Entry Swapping Bijections for Non-Attacking Fillings},
author = {Guilherme Zeus Dantas e Moura and Olya Mandelshtam},
journal= {arXiv preprint arXiv:2503.06051},
year = {2025}
}
Comments
21 pages, 11 figures, 1 table