{"title":"涉及无穷积的赫克型数列","authors":"Bing He","doi":"10.1016/j.ejc.2024.103959","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we study Hecke-type series involving infinite products. In particular, we establish some Hecke-type series involving infinite products and then obtain truncated versions of these series as well as truncated forms of some other known series of such types. Finally, as an application, we deduce six infinite families of inequalities for various partition functions. Our proofs of the main results heavily rely on a formula from the work of Liu (2013).</p></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hecke-type series involving infinite products\",\"authors\":\"Bing He\",\"doi\":\"10.1016/j.ejc.2024.103959\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we study Hecke-type series involving infinite products. In particular, we establish some Hecke-type series involving infinite products and then obtain truncated versions of these series as well as truncated forms of some other known series of such types. Finally, as an application, we deduce six infinite families of inequalities for various partition functions. Our proofs of the main results heavily rely on a formula from the work of Liu (2013).</p></div>\",\"PeriodicalId\":50490,\"journal\":{\"name\":\"European Journal of Combinatorics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-04-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Combinatorics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0195669824000441\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0195669824000441","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this paper, we study Hecke-type series involving infinite products. In particular, we establish some Hecke-type series involving infinite products and then obtain truncated versions of these series as well as truncated forms of some other known series of such types. Finally, as an application, we deduce six infinite families of inequalities for various partition functions. Our proofs of the main results heavily rely on a formula from the work of Liu (2013).
期刊介绍：
The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.
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