Compression Formula for Nonattacking Fillings of Non-symmetric Macdonald Polynomials

@misc{stewart2026compression,
  title = {{Compression Formula for Nonattacking Fillings of Non-symmetric Macdonald Polynomials}},
  author = {Alexander P. Stewart},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29950},
  eprint = {2610.29950},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29950},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Compression Formula for Nonattacking Fillings of Non-symmetric Macdonald Polynomials
AU  - Alexander P. Stewart
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29950
UR  - https://arxiv.org/abs/2610.29950
AB  - 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.
ER  -