{"title":"On the size of maximal intersecting families","authors":"D. Zakharov","doi":"10.1017/s0963548323000287","DOIUrl":null,"url":null,"abstract":"\n We show that an \n \n \n \n$n$\n\n \n -uniform maximal intersecting family has size at most \n \n \n \n$e^{-n^{0.5+o(1)}}n^n$\n\n \n . This improves a recent bound by Frankl ((2019) Comb. Probab. Comput.28(5) 733–739.). The Spread Lemma of Alweiss et al. ((2020) Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing.) plays an important role in the proof.","PeriodicalId":10503,"journal":{"name":"Combinatorics, Probability and Computing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Combinatorics, Probability and Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/s0963548323000287","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
We show that an
$n$
-uniform maximal intersecting family has size at most
$e^{-n^{0.5+o(1)}}n^n$
. This improves a recent bound by Frankl ((2019) Comb. Probab. Comput.28(5) 733–739.). The Spread Lemma of Alweiss et al. ((2020) Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing.) plays an important role in the proof.
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