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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Analytic Number Theory Research
