An Overpartition Companion of Andrews and Keith's 2-colored q-series Identity

2024/04/24 by Hunter Waldron, Waldron, Hunter
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2404.16215

openalex publication_date 2024/04/24 · openalex created_date 2024/04/27 · openalex updated_date 2026/07/28

Abstract

Andrews and Keith recently produced a general Schmidt type partition theorem using a novel interpretation of Stockhofe's bijection, which they used to find new q-series identities. This includes an identity for a trivariate 2-colored partition generating function. In this paper, their Schmidt type theorem is further generalized akin to how Franklin classically extended Glaisher's theorem. As a consequence, we obtain a companion to Andrews and Keith's 2-colored identity for overpartitions. These identities appear to be special cases of a much more general result.

Related

• A generalisation of a partition theorem of Andrews to overpartitions
• A generalisation of a second partition theorem of Andrews to overpartitions
• The combinatorics of identities involving overpartitions with distinct parts
• Combinatorial Proofs for Two-Color Partition Identities Involving Overpartitions and Minimal Excludants
• Schmidt-type theorems for partitions with uncounted parts