Generalising a finite version of Euler's partition identity
Darlison Nyirenda
TL;DR
This paper extends a finite version of Euler's partition identity by providing a generalized finite Glaisher's identity, including generating function and bijective proofs, advancing combinatorial partition theory.
Contribution
It introduces a finite generalization of Glaisher's partition identity, complementing Andrews' recent finite Euler identity proof.
Findings
Finite Glaisher's partition identity established
Generating function for the generalized identity derived
Bijective proof provided for the new identity
Abstract
Recently, George Andrews has given a Glaisher style proof of a finite version of Euler's partition identity. We generalise this result by giving a finite version of Glaisher's partition identity. Both the generating function and bijective proofs are presented.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Functional Equations Stability Results