一些可分离的整数分割类

IF 0.5 3区数学 Q3 MATHEMATICS

International Journal of Number Theory Pub Date : 2024-03-26 DOI:10.1142/s1793042124500660

Y. H. Chen, Thomas Y. He, F. Tang, J. J. Wei

{"title":"一些可分离的整数分割类","authors":"Y. H. Chen, Thomas Y. He, F. Tang, J. J. Wei","doi":"10.1142/s1793042124500660","DOIUrl":null,"url":null,"abstract":"Recently, Andrews introduced separable integer partition classes and analyzed some well-known theorems. In this paper, we investigate partitions with parts separated by parity introduced by Andrews with the aid of separable integer partition classes with modulus <math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mn>2</mn></math>. We also extend separable integer partition classes with modulus <math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mn>1</mn></math> to overpartitions, called separable overpartition classes. We study overpartitions and the overpartition analogue of Rogers–Ramanujan identities, which are separable overpartition classes.","PeriodicalId":14293,"journal":{"name":"International Journal of Number Theory","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some separable integer partition classes\",\"authors\":\"Y. H. Chen, Thomas Y. He, F. Tang, J. J. Wei\",\"doi\":\"10.1142/s1793042124500660\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Recently, Andrews introduced separable integer partition classes and analyzed some well-known theorems. In this paper, we investigate partitions with parts separated by parity introduced by Andrews with the aid of separable integer partition classes with modulus <math altimg=\\\"eq-00001.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mn>2</mn></math>. We also extend separable integer partition classes with modulus <math altimg=\\\"eq-00002.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mn>1</mn></math> to overpartitions, called separable overpartition classes. We study overpartitions and the overpartition analogue of Rogers–Ramanujan identities, which are separable overpartition classes.\",\"PeriodicalId\":14293,\"journal\":{\"name\":\"International Journal of Number Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-03-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Number Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s1793042124500660\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Number Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s1793042124500660","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

最近，安德鲁斯引入了可分离整数分区类，并分析了一些著名定理。在本文中，我们借助模数为 2 的可分离整数分区类研究安德鲁斯提出的由奇偶性分隔的分区。我们还将模为 1 的可分离整数分治类扩展为过分治，称为可分离过分治类。我们研究过分区和罗杰斯-拉马努扬等式的过分区类似物，它们都是可分离的过分区类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Some separable integer partition classes

Recently, Andrews introduced separable integer partition classes and analyzed some well-known theorems. In this paper, we investigate partitions with parts separated by parity introduced by Andrews with the aid of separable integer partition classes with modulus $2$ . We also extend separable integer partition classes with modulus $1$ to overpartitions, called separable overpartition classes. We study overpartitions and the overpartition analogue of Rogers–Ramanujan identities, which are separable overpartition classes.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

International Journal of Number Theory 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

4-8 weeks

期刊介绍： This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.