Involutions for Rogers-Ramanujan-Gordon Type Identities with Parity Restrictions
William Y.C. Chen, Doris D.M. Sang, and Diane Y.H. Shi
TL;DR
This paper develops involutions to prove Rogers-Ramanujan-Gordon type identities involving partitions with specific difference and parity restrictions, providing new combinatorial proofs for these identities.
Contribution
It introduces involutions for identities related to partitions with difference and parity restrictions, extending Andrews' work on generating functions.
Findings
Established involutions for three Rogers-Ramanujan-Gordon type identities
Provided combinatorial proofs for identities with parity restrictions
Extended the understanding of partition identities with difference constraints
Abstract
We find involutions for three Rogers-Ramanujan-Gordon type identities obtained by Andrews on the generating functions for partitions with part difference and parity restrictions.
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Advanced Combinatorial Mathematics