{"title":"用一组10个多边形平铺平面","authors":"Chao Yang","doi":"10.1142/s0218195923500012","DOIUrl":null,"url":null,"abstract":"There exists a linear algorithm to decide whether a polyomino tessellates the plane by translation only. On the other hand, the problem of deciding whether a set of [Formula: see text] or more polyominoes can tile the plane by translation is undecidable. We narrow the gap between decidable and undecidable by showing that it remains undecidable for a set of [Formula: see text] polyominoes, which partially solves a conjecture posed by Ollinger.","PeriodicalId":269811,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"142 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Tiling the Plane with a Set of Ten Polyominoes\",\"authors\":\"Chao Yang\",\"doi\":\"10.1142/s0218195923500012\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"There exists a linear algorithm to decide whether a polyomino tessellates the plane by translation only. On the other hand, the problem of deciding whether a set of [Formula: see text] or more polyominoes can tile the plane by translation is undecidable. We narrow the gap between decidable and undecidable by showing that it remains undecidable for a set of [Formula: see text] polyominoes, which partially solves a conjecture posed by Ollinger.\",\"PeriodicalId\":269811,\"journal\":{\"name\":\"International Journal of Computational Geometry & Applications\",\"volume\":\"142 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-04-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Computational Geometry & Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218195923500012\",\"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 Journal of Computational Geometry & Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218195923500012","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
There exists a linear algorithm to decide whether a polyomino tessellates the plane by translation only. On the other hand, the problem of deciding whether a set of [Formula: see text] or more polyominoes can tile the plane by translation is undecidable. We narrow the gap between decidable and undecidable by showing that it remains undecidable for a set of [Formula: see text] polyominoes, which partially solves a conjecture posed by Ollinger.
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