A modular approach to Andrews-Beck partition statistics

IF 0.9 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A Pub Date : 2023-11-15 DOI:10.1016/j.jcta.2023.105832

Renrong Mao

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引用次数: 0

Abstract

Andrews recently provided a q-series proof of congruences for $N T (m, k, n)$ , the total number of parts in the partitions of n with rank congruent to m modulo k. Motivated by Andrews' works, Chern obtain congruences for $M_{ω} (m, k, n)$ which denotes the total number of ones in the partition of n with crank congruent to m modulo k. In this paper, we focus on the modular approach to these new partition statistics. Applying the theory of mock modular forms, we establish equalities and identities for $N T (m, 7, n)$ and $M_{ω} (m, 7, n)$ .

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Andrews-Beck分区统计的模块化方法

Andrews最近给出了n的分区中秩与m模k相等的部分的总数NT(m,k,n)的同余的q级数证明。在Andrews的工作的启发下，Chern得到了m ω(m,k,n)的同余，表示n的分区中曲量与m模k相等的部分的总数。在本文中，我们重点讨论了这些新的分区统计量的模方法。应用拟模形式理论，建立了NT(m,7,n)和m ω(m,7,n)的等式和恒等式。

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

Journal of Combinatorial Theory Series A 数学-数学

CiteScore

2.90

自引率

9.10%

发文量

审稿时长

12 months

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.