{"title":"直角Coxeter群的散度和厚度特征","authors":"Ivan Levcovitz","doi":"10.1112/topo.12267","DOIUrl":null,"url":null,"abstract":"<p>We completely classify the possible divergence functions for right-angled Coxeter groups (RACGs). In particular, we show that the divergence of any such group is either polynomial, exponential, or infinite. We prove that a RACG is strongly thick of order <math>\n <semantics>\n <mi>k</mi>\n <annotation>$k$</annotation>\n </semantics></math> if and only if its divergence function is a polynomial of degree <math>\n <semantics>\n <mrow>\n <mi>k</mi>\n <mo>+</mo>\n <mn>1</mn>\n </mrow>\n <annotation>$k+1$</annotation>\n </semantics></math>. Moreover, we show that the exact divergence function of a RACG can easily be computed from its defining graph by an invariant we call the hypergraph index.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12267","citationCount":"4","resultStr":"{\"title\":\"Characterizing divergence and thickness in right-angled Coxeter groups\",\"authors\":\"Ivan Levcovitz\",\"doi\":\"10.1112/topo.12267\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We completely classify the possible divergence functions for right-angled Coxeter groups (RACGs). In particular, we show that the divergence of any such group is either polynomial, exponential, or infinite. We prove that a RACG is strongly thick of order <math>\\n <semantics>\\n <mi>k</mi>\\n <annotation>$k$</annotation>\\n </semantics></math> if and only if its divergence function is a polynomial of degree <math>\\n <semantics>\\n <mrow>\\n <mi>k</mi>\\n <mo>+</mo>\\n <mn>1</mn>\\n </mrow>\\n <annotation>$k+1$</annotation>\\n </semantics></math>. Moreover, we show that the exact divergence function of a RACG can easily be computed from its defining graph by an invariant we call the hypergraph index.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-09-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12267\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/topo.12267\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12267","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Characterizing divergence and thickness in right-angled Coxeter groups
We completely classify the possible divergence functions for right-angled Coxeter groups (RACGs). In particular, we show that the divergence of any such group is either polynomial, exponential, or infinite. We prove that a RACG is strongly thick of order if and only if its divergence function is a polynomial of degree . Moreover, we show that the exact divergence function of a RACG can easily be computed from its defining graph by an invariant we call the hypergraph index.
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