{"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}
引用次数: 0
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.
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