Bressoud–Subbarao Type Weighted Partition Identities for a Generalized Divisor Function

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Annals of Combinatorics Pub Date : 2023-04-17 DOI:10.1007/s00026-023-00647-1

Archit Agarwal, Subhash Chand Bhoria, Pramod Eyyunni, Bibekananda Maji

引用次数: 0

Abstract

In 1984, Bressoud and Subbarao obtained an interesting weighted partition identity for a generalized divisor function, by means of combinatorial arguments. Recently, the last three named authors found an analytic proof of the aforementioned identity of Bressoud and Subbarao starting from a q-series identity of Ramanujan. In the present paper, we revisit the combinatorial arguments of Bressoud and Subbarao, and derive a more general weighted partition identity. Furthermore, with the help of a fractional differential operator, we establish a few more Bressoud–Subbarao type weighted partition identities beginning from an identity of Andrews, Garvan and Liang. We also found a one-variable generalization of an identity of Uchimura related to Bell polynomials.

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广义除数函数的Bressoud–Subbarao型加权划分恒等式

1984 年，Bressoud 和 Subbarao 通过组合论证，得到了广义除数函数的一个有趣的加权分割同一性。最近，后三位作者又从拉马努扬的 q 序列同一性出发，找到了对 Bressoud 和 Subbarao 上述同一性的解析证明。在本文中，我们重温了 Bressoud 和 Subbarao 的组合论证，并推导出一个更一般的加权分割同一性。此外，在分数微分算子的帮助下，我们从安德鲁斯、加万和梁的一个特征出发，建立了更多的布列索德-苏巴拉奥类型的加权分割特征。我们还发现了与贝尔多项式有关的内村特性的一变量广义化。

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

Annals of Combinatorics 数学-应用数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annals of Combinatorics publishes outstanding contributions to combinatorics with a particular focus on algebraic and analytic combinatorics, as well as the areas of graph and matroid theory. Special regard will be given to new developments and topics of current interest to the community represented by our editorial board. The scope of Annals of Combinatorics is covered by the following three tracks: Algebraic Combinatorics: Enumerative combinatorics, symmetric functions, Schubert calculus / Combinatorial Hopf algebras, cluster algebras, Lie algebras, root systems, Coxeter groups / Discrete geometry, tropical geometry / Discrete dynamical systems / Posets and lattices Analytic and Algorithmic Combinatorics: Asymptotic analysis of counting sequences / Bijective combinatorics / Univariate and multivariable singularity analysis / Combinatorics and differential equations / Resolution of hard combinatorial problems by making essential use of computers / Advanced methods for evaluating counting sequences or combinatorial constants / Complexity and decidability aspects of combinatorial sequences / Combinatorial aspects of the analysis of algorithms Graphs and Matroids: Structural graph theory, graph minors, graph sparsity, decompositions and colorings / Planar graphs and topological graph theory, geometric representations of graphs / Directed graphs, posets / Metric graph theory / Spectral and algebraic graph theory / Random graphs, extremal graph theory / Matroids, oriented matroids, matroid minors / Algorithmic approaches