{"title":"Tiling with Monotone Polyominos","authors":"István Tomon","doi":"10.1080/00029890.2023.2265284","DOIUrl":null,"url":null,"abstract":"AbstractA monotone polyomino is a set of grid cells pierced by a continuous monotone function f:[a,b]→R. We prove that the minimum number of monotone polyominos in a tiling of the n×n lattice square is n. Surprisingly, this turns out to be equivalent with the statement that every triangulation of the n×n lattice square into minimum lattice triangles contains at least 2n right angled triangles.MSC: 05B5005B45 ACKNOWLEDGMENTSThe author wishes to thank Christian Richter and the anonymous referees for their useful comments and suggestions.Additional informationNotes on contributorsIstván TomonISTVÁN TOMON received his Ph.D. in mathematics from the University of Cambridge. He spent several years as a postdoctoral student at the EPFL and ETH Zurich. Currently, he is an Associate Professor at Umeå University, pursuing research in combinatorics and related areas.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Mathematical Monthly","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/00029890.2023.2265284","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
AbstractA monotone polyomino is a set of grid cells pierced by a continuous monotone function f:[a,b]→R. We prove that the minimum number of monotone polyominos in a tiling of the n×n lattice square is n. Surprisingly, this turns out to be equivalent with the statement that every triangulation of the n×n lattice square into minimum lattice triangles contains at least 2n right angled triangles.MSC: 05B5005B45 ACKNOWLEDGMENTSThe author wishes to thank Christian Richter and the anonymous referees for their useful comments and suggestions.Additional informationNotes on contributorsIstván TomonISTVÁN TOMON received his Ph.D. in mathematics from the University of Cambridge. He spent several years as a postdoctoral student at the EPFL and ETH Zurich. Currently, he is an Associate Professor at Umeå University, pursuing research in combinatorics and related areas.
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