{"docId":6596,"paperId":6022,"url":"https:\/\/dmtcs.episciences.org\/6022","doi":"10.23638\/DMTCS-22-1-21","journalName":"Discrete Mathematics & Theoretical Computer Science","issn":"","eissn":"1365-8050","volume":[{"vid":372,"name":"vol. 22 no. 1"}],"section":[{"sid":6,"title":"Combinatorics","description":[]}],"repositoryName":"arXiv","repositoryIdentifier":"2001.03289","repositoryVersion":3,"repositoryLink":"https:\/\/arxiv.org\/abs\/2001.03289v3","dateSubmitted":"2020-01-13 03:55:40","dateAccepted":"2020-06-29 15:34:23","datePublished":"2020-06-29 15:34:40","titles":["Dissecting a square into congruent polygons"],"authors":["Rao, Hui","Ren, Lei","Wang, Yang"],"abstracts":["We study the dissection of a square into congruent convex polygons. Yuan \\emph{et al.} [Dissecting the square into five congruent parts, Discrete Math. \\textbf{339} (2016) 288-298] asked whether, if the number of tiles is a prime number $\\geq 3$, it is true that the tile must be a rectangle. We conjecture that the same conclusion still holds even if the number of tiles is an odd number $\\geq 3$. Our conjecture has been confirmed for triangles in earlier works. We prove that the conjecture holds if either the tile is a convex $q$-gon with $q\\geq 6$ or it is a right-angle trapezoid.","Comment: 19 pages, 11 figure"],"keywords":["Mathematics - Combinatorics","52B45, 05C45"]}