Tiling with Monotone Polyominos

IF 0.4 4区数学 Q4 MATHEMATICS

American Mathematical Monthly Pub Date : 2023-10-11 DOI:10.1080/00029890.2023.2265284

István Tomon

引用次数: 0

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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用单调多聚子平铺

单调多多项式是由连续单调函数f:[a,b]→R刺穿的网格单元集。我们证明了在n×n格子正方形的一个平铺中，单调多项式的最小数目是n。令人惊讶的是，这与下述陈述是等价的:n×n格子正方形的每一个三角剖分都包含至少2n个直角三角形。作者要感谢Christian Richter和匿名审稿人提供的有用的意见和建议。关于contributorsIstván TomonISTVÁN的说明TOMON在剑桥大学获得数学博士学位。他在EPFL和苏黎世联邦理工学院做了几年的博士后。目前，他是尤梅夫大学副教授，从事组合学及相关领域的研究。

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来源期刊

American Mathematical Monthly Mathematics-General Mathematics

CiteScore

0.80

自引率

20.00%

发文量

127

审稿时长

6-12 weeks

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