{"title":"具有全局n折旋转对称的切割投影菱形瓷砖的有效构造","authors":"Victor H. Lutfalla","doi":"10.4230/OASIcs.AUTOMATA.2021.9","DOIUrl":null,"url":null,"abstract":"We give an explicit and effective construction for rhombus cut-and-project tilings with global n-fold rotational symmetry for any n. This construction is based on the dualization of regular n-fold multigrids. The main point is to prove the regularity of these multigrids, for this we use a result on trigonometric diophantine equations. A SageMath program that computes these tilings and outputs svg files is publicly available in [7]. 2012 ACM Subject Classification Mathematics of computing → Discrete mathematics; Mathematics of computing → Combinatorics","PeriodicalId":124625,"journal":{"name":"International Workshop on Cellular Automata and Discrete Complex Systems","volume":" 5","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"An Effective Construction for Cut-And-Project Rhombus Tilings with Global n-Fold Rotational Symmetry\",\"authors\":\"Victor H. Lutfalla\",\"doi\":\"10.4230/OASIcs.AUTOMATA.2021.9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give an explicit and effective construction for rhombus cut-and-project tilings with global n-fold rotational symmetry for any n. This construction is based on the dualization of regular n-fold multigrids. The main point is to prove the regularity of these multigrids, for this we use a result on trigonometric diophantine equations. A SageMath program that computes these tilings and outputs svg files is publicly available in [7]. 2012 ACM Subject Classification Mathematics of computing → Discrete mathematics; Mathematics of computing → Combinatorics\",\"PeriodicalId\":124625,\"journal\":{\"name\":\"International Workshop on Cellular Automata and Discrete Complex Systems\",\"volume\":\" 5\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Workshop on Cellular Automata and Discrete Complex Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4230/OASIcs.AUTOMATA.2021.9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Workshop on Cellular Automata and Discrete Complex Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4230/OASIcs.AUTOMATA.2021.9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An Effective Construction for Cut-And-Project Rhombus Tilings with Global n-Fold Rotational Symmetry
We give an explicit and effective construction for rhombus cut-and-project tilings with global n-fold rotational symmetry for any n. This construction is based on the dualization of regular n-fold multigrids. The main point is to prove the regularity of these multigrids, for this we use a result on trigonometric diophantine equations. A SageMath program that computes these tilings and outputs svg files is publicly available in [7]. 2012 ACM Subject Classification Mathematics of computing → Discrete mathematics; Mathematics of computing → Combinatorics
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