On odd ranks of odd Durfee symbols

Author:

Cui Su-Ping12,Gu Nancy S. S.3ORCID

Affiliation:

1. School of Mathematics and Statistics, Qinghai Normal University, Xining, Qinghai 810008, P. R. China

2. Academy of Plateau Science and Sustainability, Xining, Qinghai 810008, P. R. China

3. Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, P. R. China

Abstract

An odd Durfee symbol of [Formula: see text] is an array of positive odd integers and a subscript [Formula: see text], [Formula: see text] such that [Formula: see text], [Formula: see text], and [Formula: see text]. Andrews defined the odd rank of an odd Durfee symbol as [Formula: see text]. Let [Formula: see text] be the number of odd Durfee symbols of [Formula: see text] with odd rank congruent to [Formula: see text] modulo [Formula: see text]. We decompose the generating function of [Formula: see text] into modular and mock modular parts. Specifically, we derive some special cases of the generating functions of [Formula: see text] for [Formula: see text]. Some generating functions are related to classical mock theta functions.

Funder

National Natural Science Foundation of China

Fundamental Research Funds for the Central Universities

Foreign Youth Exchange Program of China Association of Science and Technology

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Modular forms and congruences for k-marked odd Durfee symbols;Journal of Mathematical Analysis and Applications;2024-12

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