{"title":"上巴拿赫密度定理的组合证明","authors":"Boxu Huang","doi":"10.1007/s40840-024-01671-x","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we introduce a combinatorial proof approach for a theorem regarding the upper Banach density of a subset <i>S</i> of <span>\\({\\mathbb {N}}\\)</span> and present a finite IP-set revision of the theorem originally established by Li, Tu, and Ye.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Combinational Proof for a Theorem Concerning the Upper Banach Density\",\"authors\":\"Boxu Huang\",\"doi\":\"10.1007/s40840-024-01671-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we introduce a combinatorial proof approach for a theorem regarding the upper Banach density of a subset <i>S</i> of <span>\\\\({\\\\mathbb {N}}\\\\)</span> and present a finite IP-set revision of the theorem originally established by Li, Tu, and Ye.</p>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-03-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s40840-024-01671-x\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40840-024-01671-x","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
本文介绍了关于 \({\mathbb {N}}\) 子集 S 的上巴纳赫密度定理的组合证明方法，并提出了对最初由 Li、Tu 和 Ye 建立的定理的有限 IP 集修正。
Combinational Proof for a Theorem Concerning the Upper Banach Density
In this paper, we introduce a combinatorial proof approach for a theorem regarding the upper Banach density of a subset S of \({\mathbb {N}}\) and present a finite IP-set revision of the theorem originally established by Li, Tu, and Ye.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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