Refinements of the Rogers-Ramanujan identities
Kathleen O'Hara, Dennis Stanton
TL;DR
This paper presents refined versions of the Rogers-Ramanujan identities with weighted components, offering new combinatorial interpretations that extend MacMahon's classical results.
Contribution
It introduces weighted refinements of the Rogers-Ramanujan identities and provides combinatorial interpretations that enhance existing classical results.
Findings
Weighted Rogers-Ramanujan identities derived
New combinatorial interpretations established
Extensions of MacMahon's results achieved
Abstract
Refinements of the classical Rogers-Ramanujan identities are given in which some parts are weighted. Combinatorial interpretations refining MacMahon's results are corollaries.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Analytic Number Theory Research