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}
}