A Weighted Words Study of MacMahon's and Russell's Modulo 6 Identities
Combinatorics
2026-02-18 v1 Number Theory
Abstract
We give new proofs of MacMahon and Russell's modulo 6 identities using the method of weighted words. We also present a new refinement of MacMahon's identity, some related finite sum identities, and a companion partition theorem to sequence avoiding partitions theorem of the author and Andrews.
Cite
@article{arxiv.2602.15232,
title = {A Weighted Words Study of MacMahon's and Russell's Modulo 6 Identities},
author = {Ali K. Uncu},
journal= {arXiv preprint arXiv:2602.15232},
year = {2026}
}
Comments
13 pages, 2 tables, Happy Birthday to K Alladi