balantine、Feigon和Merca关于奇部分区线性不等式的四个猜想的证明

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2025-05-14 DOI:10.1016/j.jnt.2025.03.014

Olivia X.M. Yao

{"title":"balantine、Feigon和Merca关于奇部分区线性不等式的四个猜想的证明","authors":"Olivia X.M. Yao","doi":"10.1016/j.jnt.2025.03.014","DOIUrl":null,"url":null,"abstract":"<div><div>In their seminal work, Andrews and Merca studied the truncated version of Euler's pentagonal number theorem and deduced an infinite family of linear inequalities for ordinary partition function. The work of Andrews and Merca opened up the study of truncated theta series and linear inequalities for certain restricted partition functions and many articles followed. Recently, Ballantine and Feigon, and Merca posed four conjectures on linear inequalities for partitions with odd parts. In this paper, we confirm those conjectures based on a classical result contributed to Pólya and Szegő.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"277 ","pages":"Pages 344-368"},"PeriodicalIF":0.6000,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Proofs of four conjectures of Ballantine, Feigon and Merca on linear inequalities of partitions with odd parts\",\"authors\":\"Olivia X.M. Yao\",\"doi\":\"10.1016/j.jnt.2025.03.014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In their seminal work, Andrews and Merca studied the truncated version of Euler's pentagonal number theorem and deduced an infinite family of linear inequalities for ordinary partition function. The work of Andrews and Merca opened up the study of truncated theta series and linear inequalities for certain restricted partition functions and many articles followed. Recently, Ballantine and Feigon, and Merca posed four conjectures on linear inequalities for partitions with odd parts. In this paper, we confirm those conjectures based on a classical result contributed to Pólya and Szegő.</div></div>\",\"PeriodicalId\":50110,\"journal\":{\"name\":\"Journal of Number Theory\",\"volume\":\"277 \",\"pages\":\"Pages 344-368\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2025-05-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Number Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022314X25001271\",\"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":"Journal of Number Theory","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022314X25001271","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

在他们的开创性工作中，Andrews和Merca研究了欧拉五边形数定理的删节版，并推导了普通配分函数的无限线性不等式族。Andrews和Merca的工作开启了截断级数和某些受限配分函数的线性不等式的研究，并随后发表了许多文章。最近，Ballantine和Feigon以及Merca对奇部分区的线性不等式提出了四个猜想。在本文中，我们根据Pólya和塞格格的经典结果证实了这些猜想。

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

Proofs of four conjectures of Ballantine, Feigon and Merca on linear inequalities of partitions with odd parts

In their seminal work, Andrews and Merca studied the truncated version of Euler's pentagonal number theorem and deduced an infinite family of linear inequalities for ordinary partition function. The work of Andrews and Merca opened up the study of truncated theta series and linear inequalities for certain restricted partition functions and many articles followed. Recently, Ballantine and Feigon, and Merca posed four conjectures on linear inequalities for partitions with odd parts. In this paper, we confirm those conjectures based on a classical result contributed to Pólya and Szegő.

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

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.