A Weighted Words Study of MacMahon's and Russell's Modulo 6 Identities
Ali K. Uncu
TL;DR
This paper introduces new proofs of classical modulo 6 identities using weighted words, along with a refinement, related identities, and a partition theorem, advancing combinatorial partition theory.
Contribution
It provides novel proofs and refinements of MacMahon and Russell's identities through weighted words, and introduces related finite sum identities and a new partition theorem.
Findings
New proofs of MacMahon and Russell's identities
Refinement of MacMahon's identity
A companion partition theorem
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.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Analytic Number Theory Research