{"title":"将$5\\乘以5$数组划分为圆的限制","authors":"R. Dawson","doi":"10.11575/CDM.V15I1.62808","DOIUrl":null,"url":null,"abstract":"We show that there is a unique way to partition a $5\\times 5$ array of lattice points into restrictions of five circles. This result is extended to the $6\\times 5$ array, and used to show the optimality of a six-circle solution for the $6\\times 6$ array.","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2020-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Partitioning the $5\\\\times 5$ array into restrictions of circles\",\"authors\":\"R. Dawson\",\"doi\":\"10.11575/CDM.V15I1.62808\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that there is a unique way to partition a $5\\\\times 5$ array of lattice points into restrictions of five circles. This result is extended to the $6\\\\times 5$ array, and used to show the optimality of a six-circle solution for the $6\\\\times 6$ array.\",\"PeriodicalId\":48938,\"journal\":{\"name\":\"Contributions To Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-05-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Contributions To Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.11575/CDM.V15I1.62808\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Contributions To Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.11575/CDM.V15I1.62808","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Partitioning the $5\times 5$ array into restrictions of circles
We show that there is a unique way to partition a $5\times 5$ array of lattice points into restrictions of five circles. This result is extended to the $6\times 5$ array, and used to show the optimality of a six-circle solution for the $6\times 6$ array.
期刊介绍:
Contributions to Discrete Mathematics (ISSN 1715-0868) is a refereed e-journal dedicated to publishing significant results in a number of areas of pure and applied mathematics. Based at the University of Calgary, Canada, CDM is free for both readers and authors, edited and published online and will be mirrored at the European Mathematical Information Service and the National Library of Canada.