An overpartition companion of Andrews and Keith's 2-colored q-series identity

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 t...

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Bibliographic Details
Published inDiscrete mathematics Vol. 348; no. 12; p. 114651
Main Author Waldron, Hunter
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2025
Subjects
05A17
Bijective combinatorics
Partitions
Q-series
Partitions
Q-series
Bijective combinatorics
05A17
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Summary: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.
ISSN:0012-365X
DOI:10.1016/j.disc.2025.114651