{"title":"Spherical configurations over finite fields","authors":"N. Lyall, Á. Magyar, Hans Parshall","doi":"10.1353/ajm.2020.0010","DOIUrl":null,"url":null,"abstract":"abstract:We establish that if $d\\geq 2k+6$ and $q$ is odd and sufficiently large with respect to $\\alpha\\in (0,1)$, then every set $A\\subseteq{\\bf F}_q^d$of size $|A|\\geq\\alpha q^d$ will contain an isometric copy of every spherical $(k+2)$-point configuration that spans $k$ dimensions.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"142 1","pages":"373 - 404"},"PeriodicalIF":1.7000,"publicationDate":"2020-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1353/ajm.2020.0010","citationCount":"12","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1353/ajm.2020.0010","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 12
Abstract
abstract:We establish that if $d\geq 2k+6$ and $q$ is odd and sufficiently large with respect to $\alpha\in (0,1)$, then every set $A\subseteq{\bf F}_q^d$of size $|A|\geq\alpha q^d$ will contain an isometric copy of every spherical $(k+2)$-point configuration that spans $k$ dimensions.
期刊介绍：
The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.
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