A Partition Function Connected with the G\"ollnitz--Gordon Identities
Nicolas Allen Smoot
TL;DR
This paper applies the circle method to derive convergent formulas for counting specific partitions related to the G"ollnitz--Gordon identities, advancing the understanding of these combinatorial structures.
Contribution
It introduces a novel application of the circle method to obtain explicit formulas for partition counts associated with G"ollnitz--Gordon identities.
Findings
Derived convergent formulas for partition counts
Connected circle method with G"ollnitz--Gordon identities
Enhanced analytical tools for partition enumeration
Abstract
We use the celebrated circle method of Hardy and Ramanujan to develop convergent formulae for counting a restricted class of partitions that arise from the G\"ollnitz--Gordon identities.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Analytic Number Theory Research