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

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-06-26 DOI:10.1016/j.disc.2025.114651

Hunter Waldron

引用次数: 0

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.

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Andrews和Keith的二色q级数恒等式的一个过划分伴侣

Andrews和Keith最近利用对Stockhofe双射的一种新的解释，提出了一个一般的Schmidt型划分定理，他们用它来寻找新的q级数恒等式。这包括一个三元2色分区生成函数的恒等式。本文进一步推广了他们的Schmidt型定理，类似于Franklin对Glaisher定理的经典推广。因此，我们得到了Andrews和Keith关于过度分割的二色恒等式的一个同伴。这些恒等式似乎是一个更一般结果的特殊情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.