English

A refinement of and a companion to MacMahon's partition identity

Combinatorics 2023-08-01 v1 Number Theory

Abstract

We provide a refinement of MacMahon's partition identity on sequence-avoiding partitions, and use it to produce another mod 6 partition identity. In addition, we show that our technique also extends to cover Andrews's generalization of MacMahon's identity. Our proofs are bijective in nature, exploiting a theorem of Xiong and Keith.

Keywords

Cite

@article{arxiv.2307.16753,
  title  = {A refinement of and a companion to MacMahon's partition identity},
  author = {Matthew C. Russell},
  journal= {arXiv preprint arXiv:2307.16753},
  year   = {2023}
}