Marcin Briański, Jȩdrzej Hodor, Hoang La, Piotr Micek, Katzper Michno
{"title":"布尔网格的布尔维度","authors":"Marcin Briański, Jȩdrzej Hodor, Hoang La, Piotr Micek, Katzper Michno","doi":"10.1007/s11083-024-09666-w","DOIUrl":null,"url":null,"abstract":"<p>For every integer <i>n</i> with <span>\\(n \\geqslant 6\\)</span>, we prove that the Boolean dimension of a poset consisting of all the subsets of <span>\\(\\{1,\\dots ,n\\}\\)</span> equipped with the inclusion relation is strictly less than <i>n</i>.</p>","PeriodicalId":501237,"journal":{"name":"Order","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Boolean Dimension of a Boolean Lattice\",\"authors\":\"Marcin Briański, Jȩdrzej Hodor, Hoang La, Piotr Micek, Katzper Michno\",\"doi\":\"10.1007/s11083-024-09666-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>For every integer <i>n</i> with <span>\\\\(n \\\\geqslant 6\\\\)</span>, we prove that the Boolean dimension of a poset consisting of all the subsets of <span>\\\\(\\\\{1,\\\\dots ,n\\\\}\\\\)</span> equipped with the inclusion relation is strictly less than <i>n</i>.</p>\",\"PeriodicalId\":501237,\"journal\":{\"name\":\"Order\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Order\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s11083-024-09666-w\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Order","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11083-024-09666-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
For every integer n with \(n \geqslant 6\), we prove that the Boolean dimension of a poset consisting of all the subsets of \(\{1,\dots ,n\}\) equipped with the inclusion relation is strictly less than n.