{"title":"最大正方形平面上的单色三角形","authors":"Alexander Natalchenko , Arsenii Sagdeev","doi":"10.1016/j.ejc.2024.103977","DOIUrl":null,"url":null,"abstract":"<div><p>For all non-degenerate triangles <span><math><mi>T</mi></math></span>, we determine the minimum number of colors needed to color the plane such that no max-norm isometric copy of <span><math><mi>T</mi></math></span> is monochromatic.</p></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Monochromatic triangles in the max-norm plane\",\"authors\":\"Alexander Natalchenko , Arsenii Sagdeev\",\"doi\":\"10.1016/j.ejc.2024.103977\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>For all non-degenerate triangles <span><math><mi>T</mi></math></span>, we determine the minimum number of colors needed to color the plane such that no max-norm isometric copy of <span><math><mi>T</mi></math></span> is monochromatic.</p></div>\",\"PeriodicalId\":50490,\"journal\":{\"name\":\"European Journal of Combinatorics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-05-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Combinatorics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0195669824000623\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0195669824000623","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
对于所有非退化三角形 T,我们要确定给平面着色所需的最少颜色数,从而使 T 的最大等距副本都不是单色的。
For all non-degenerate triangles , we determine the minimum number of colors needed to color the plane such that no max-norm isometric copy of is monochromatic.
期刊介绍:
The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.