Notes for Neighborly Partitions
Kathleen O'Hara, Dennis Stanton
TL;DR
This paper presents a proof of the first Rogers-Ramanujan identity using admissible neighborly partitions with a special mod 3 condition, completing a previously initiated mathematical program.
Contribution
It introduces a novel approach with admissible neighborly partitions involving a unique mod 3 condition, providing a new proof of a classical identity.
Findings
Proof of the first Rogers-Ramanujan identity established
Introduces admissible neighborly partitions with a mod 3 condition
Completes a mathematical program initiated by Mohsen and Mourtada
Abstract
A proof of the first Rogers-Ramanujan identity is given using admissible neighborly partitions. This completes a program initiated by Mohsen and Mourtada. The admissible neighborly partitions involve an unusual mod 3 condition on the parts.
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Advanced Combinatorial Mathematics