MacMahon's partition analysis XIV: Partitions with n copies of n

被引：2

作者：

Andrews, George E. ^{[1
]}

Paule, Peter ^{[2
]}

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[2] Johannes Kepler Univ Linz, Res Inst Symbol Computat RISC, A-4040 Linz, Austria

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2024年 / 203卷

基金：

奥地利科学基金会;

关键词：

Partitions; Overpartitions; Partitions with n copies of n; Partition analysis; q-series; Modular forms and partition; congruences; Radu's Ramanujan-Kolb erg; algorithm; RAMANUJAN; IDENTITIES;

D O I：

10.1016/j.jcta.2023.105836

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We apply the methods of partition analysis to partitions with n copies of n. This allows us to obtain multivariable generating functions related to classical Rogers-Ramanujan type identities. Also, partitions with n copies of n are extended to partition diamonds yielding numerous new results including a natural connection to overpartitions and a variety of partition congruences. (c) 2023 Elsevier Inc. All rights reserved.

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页数：34

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