Probabilistic Entry Swapping Bijections for Non-Attacking Fillings
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909531720646656 |
|---|---|
| author | Moura, Guilherme Zeus Dantas e Mandelshtam, Olya |
| author_facet | Moura, Guilherme Zeus Dantas e Mandelshtam, Olya |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06051 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Probabilistic Entry Swapping Bijections for Non-Attacking Fillings Moura, Guilherme Zeus Dantas e Mandelshtam, Olya Combinatorics 05E05, 05A19, 33D52 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. |
| title | Probabilistic Entry Swapping Bijections for Non-Attacking Fillings |
| topic | Combinatorics 05E05, 05A19, 33D52 |
| url | https://arxiv.org/abs/2503.06051 |