{"title":"On the Local-Global Conjecture for Combinatorial Period Lengths of Closed Billiards on the Regular Pentagon","authors":"Alex Kontorovich, Xin Zhang","doi":"arxiv-2409.10682","DOIUrl":null,"url":null,"abstract":"We study the set of combinatorial lengths of asymmetric periodic trajectories\non the regular pentagon, proving a density-one version of a conjecture of\nDavis-Lelievre.","PeriodicalId":501064,"journal":{"name":"arXiv - MATH - Number Theory","volume":"14 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Number Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10682","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
We study the set of combinatorial lengths of asymmetric periodic trajectories
on the regular pentagon, proving a density-one version of a conjecture of
Davis-Lelievre.
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