Ramanujan的Theta函数与分部的奇偶性和分区的曲柄。

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED Annals of Combinatorics Pub Date : 2022-10-25 DOI:10.1007/s00026-022-00615-1

Koustav Banerjee, Manosij Ghosh Dastidar

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引用次数: 3

摘要

在本文中，我们探讨了Ramanujanθ函数和一类由其部分奇偶性定义的配分函数之间的复杂联系。因此，我们可以对分区的曲柄进行奇偶性分析，以及它与具有奇数部分的分区数、自共轭分区以及与Durfee平方和Frobenius符号的相关性。

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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Ramanujan’s Theta Functions and Parity of Parts and Cranks of Partitions

In this paper, we explore intricate connections between Ramanujan’s theta functions and a class of partition functions defined by the nature of the parity of their parts. This consequently leads us to the parity analysis of the crank of a partition and its correlation with the number of partitions with odd number of parts, self-conjugate partitions, and also with Durfee squares and Frobenius symbols.

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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

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