{"title":"A new construction of forests with low visibility","authors":"Kirill Kashkan","doi":"10.1112/mtk.70013","DOIUrl":null,"url":null,"abstract":"<p>A set of points with finite density is constructed in <span></span><math></math>, with <span></span><math></math>, by adding points to a Poisson process such that any line segment of length <span></span><math></math> in <span></span><math></math> will contain one of the points of the set within distance <span></span><math></math> of it. The constant implied by the big-<span></span><math></math> notation depends on the dimension only.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 2","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70013","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematika","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/mtk.70013","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
A set of points with finite density is constructed in , with , by adding points to a Poisson process such that any line segment of length in will contain one of the points of the set within distance of it. The constant implied by the big- notation depends on the dimension only.
期刊介绍：
Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.
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