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

被引：2

作者：

Banerjee, Koustav ^{[1
]}

Dastidar, Manosij Ghosh ^{[2
]}

机构：

[1] Johannes Kepler Univ Linz, Res Inst Symbol Computat, Altenberger Str 69, A-4040 Linz, Austria

[2] Tech Univ Wien, Wiedner Hauptstr 810-104, A-1040 Vienna, Austria

来源：

ANNALS OF COMBINATORICS | 2023年 / 27卷 / 03期

基金：

奥地利科学基金会;

关键词：

Ramanujan's theta functions; Partitions; Parity of parts; Cranks;

D O I：

10.1007/s00026-022-00615-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：565 / 578

页数：14

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