Euler's partition theorem for all moduli and new companions to Rogers-Ramanujan-Andrews-Gordon identities
XinHua Xiong, William J. Keith
TL;DR
This paper generalizes Euler's partition theorem to all moduli and introduces new companions to the Rogers-Ramanujan-Andrews-Gordon identities, expanding the understanding of partition identities.
Contribution
It extends Euler's partition theorem to all moduli and offers new identities related to Rogers-Ramanujan-Andrews-Gordon identities.
Findings
Generalization of Euler's theorem for all moduli
New identities related to Rogers-Ramanujan-Andrews-Gordon identities
Broader framework for partition theorems
Abstract
We generalise Euler's partition theorem involving odd parts and different parts for all moduli and provide new companions to Rogers-Ramanujan- Andrews-Gordon identities related to this theorem.
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Advanced Combinatorial Mathematics