{"title":"关于五维吻合安排的说明","authors":"Ferenc Szöllősi","doi":"10.4310/mrl.2023.v30.n5.a13","DOIUrl":null,"url":null,"abstract":"The kissing number $\\tau (d)$ is the maximum number of pairwise non-overlapping unit spheres each touching a central unit sphere in the $d$-dimensional Euclidean space. In this note we report on how we discovered a new, previously unknown arrangement of 40 unit spheres in dimension $5$. Our arrangement saturates the best known lower bound on $\\tau (5)$, and refutes a ‘belief’ of Cohn–Jiao–Kumar–Torquato.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"77 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A note on five dimensional kissing arrangements\",\"authors\":\"Ferenc Szöllősi\",\"doi\":\"10.4310/mrl.2023.v30.n5.a13\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The kissing number $\\\\tau (d)$ is the maximum number of pairwise non-overlapping unit spheres each touching a central unit sphere in the $d$-dimensional Euclidean space. In this note we report on how we discovered a new, previously unknown arrangement of 40 unit spheres in dimension $5$. Our arrangement saturates the best known lower bound on $\\\\tau (5)$, and refutes a ‘belief’ of Cohn–Jiao–Kumar–Torquato.\",\"PeriodicalId\":49857,\"journal\":{\"name\":\"Mathematical Research Letters\",\"volume\":\"77 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-05-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Research Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/mrl.2023.v30.n5.a13\",\"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":"Mathematical Research Letters","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/mrl.2023.v30.n5.a13","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
The kissing number $\tau (d)$ is the maximum number of pairwise non-overlapping unit spheres each touching a central unit sphere in the $d$-dimensional Euclidean space. In this note we report on how we discovered a new, previously unknown arrangement of 40 unit spheres in dimension $5$. Our arrangement saturates the best known lower bound on $\tau (5)$, and refutes a ‘belief’ of Cohn–Jiao–Kumar–Torquato.
期刊介绍:
Dedicated to publication of complete and important papers of original research in all areas of mathematics. Expository papers and research announcements of exceptional interest are also occasionally published. High standards are applied in evaluating submissions; the entire editorial board must approve the acceptance of any paper.