{"title":"MacMahon's partition analysis XIV: Partitions with n copies of n","authors":"George E. Andrews , Peter Paule","doi":"10.1016/j.jcta.2023.105836","DOIUrl":null,"url":null,"abstract":"<div><p>We apply the methods of partition analysis to partitions with <em>n</em> copies of <em>n</em>. This allows us to obtain multivariable generating functions related to classical Rogers-Ramanujan type identities. Also, partitions with <em>n</em> copies of <em>n</em> are extended to partition diamonds yielding numerous new results including a natural connection to overpartitions and a variety of partition congruences.</p></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"203 ","pages":"Article 105836"},"PeriodicalIF":0.9000,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series A","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0097316523001048","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.
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