{"title":"5 核和 7 核分区的新无限同余族","authors":"Z. Meng, O. X. M. Yao","doi":"10.1007/s10474-024-01424-z","DOIUrl":null,"url":null,"abstract":"<div><p>Let <span>\\(a_t(n)\\)</span> denote the number of <i>t</i>-core partitions of <i>n</i>. In recent years, a number of congruences for <span>\\(a_t(n)\\)</span> have been discovered for some small <i>t</i>. Very recently, Fathima and Pore [4] established infinite families of congruences modulo 3 for <span>\\(a_5(n)\\)</span> and congruences modulo 2 for <span>\\(a_7(n)\\)</span>. Motivated by their work, we prove some new infinite families of congruences modulo 3 for <span>\\(a_5(n)\\)</span> and congruences modulo 2 for <span>\\(a_7(n)\\)</span> by utilizing Newman's identities.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"New infinite families of congruences for 5-core and 7-core partitions\",\"authors\":\"Z. Meng, O. X. M. Yao\",\"doi\":\"10.1007/s10474-024-01424-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <span>\\\\(a_t(n)\\\\)</span> denote the number of <i>t</i>-core partitions of <i>n</i>. In recent years, a number of congruences for <span>\\\\(a_t(n)\\\\)</span> have been discovered for some small <i>t</i>. Very recently, Fathima and Pore [4] established infinite families of congruences modulo 3 for <span>\\\\(a_5(n)\\\\)</span> and congruences modulo 2 for <span>\\\\(a_7(n)\\\\)</span>. Motivated by their work, we prove some new infinite families of congruences modulo 3 for <span>\\\\(a_5(n)\\\\)</span> and congruences modulo 2 for <span>\\\\(a_7(n)\\\\)</span> by utilizing Newman's identities.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-04-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10474-024-01424-z\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10474-024-01424-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
New infinite families of congruences for 5-core and 7-core partitions
Let \(a_t(n)\) denote the number of t-core partitions of n. In recent years, a number of congruences for \(a_t(n)\) have been discovered for some small t. Very recently, Fathima and Pore [4] established infinite families of congruences modulo 3 for \(a_5(n)\) and congruences modulo 2 for \(a_7(n)\). Motivated by their work, we prove some new infinite families of congruences modulo 3 for \(a_5(n)\) and congruences modulo 2 for \(a_7(n)\) by utilizing Newman's identities.
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