A bijection related to Bressoud's conjecture

Y. H. Chen; Thomas Y. He

A bijection related to Bressoud's conjecture

Combinatorics 2024-05-31 v1

Authors: Y. H. Chen , Thomas Y. He

Abstract

Bressoud introduced the partition function $B(\alpha_1,\ldots,\alpha_\lambda;\eta,k,r;n)$ , which counts the number of partitions with certain difference conditions. Bressoud posed a conjecture on the generating function for the partition function $B(\alpha_1,\ldots,\alpha_\lambda;\eta,k,r;n)$ in multi-summation form. In this article, we introduce a bijection related to Bressoud's conjecture. As an application, we give a new companion to the G\"ollnitz-Gordon identities.

Keywords

partition theory partition congruences bijective combinatorics

Cite

@article{arxiv.2405.19918,
  title  = {A bijection related to Bressoud's conjecture},
  author = {Y. H. Chen and Thomas Y. He},
  journal= {arXiv preprint arXiv:2405.19918},
  year   = {2024}
}

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