{"title":"最小奇数不等式和欧拉分割定理","authors":"Andrew Y. Z. Wang, Zheng Xu","doi":"10.1142/s1793042124500714","DOIUrl":null,"url":null,"abstract":"<p>In this work, we establish two interesting partition identities involving the minimal odd excludant, which has attracted great attention in recent years. In particular, we find a strong refinement of Euler’s celebrated theorem that the number of partitions of an integer into odd parts equals the number of partitions of that integer into distinct parts.</p>","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\":\"The minimal odd excludant and Euler’s partition theorem\",\"authors\":\"Andrew Y. Z. Wang, Zheng Xu\",\"doi\":\"10.1142/s1793042124500714\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this work, we establish two interesting partition identities involving the minimal odd excludant, which has attracted great attention in recent years. In particular, we find a strong refinement of Euler’s celebrated theorem that the number of partitions of an integer into odd parts equals the number of partitions of that integer into distinct parts.</p>\",\"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/s1793042124500714\",\"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/s1793042124500714","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
The minimal odd excludant and Euler’s partition theorem
In this work, we establish two interesting partition identities involving the minimal odd excludant, which has attracted great attention in recent years. In particular, we find a strong refinement of Euler’s celebrated theorem that the number of partitions of an integer into odd parts equals the number of partitions of that integer into distinct parts.
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.