{"title":"On the Statistics of Dimer Coverings and Spanning Trees on the Silicate-Type Sierpinski Gasket","authors":"Xingsheng Yang, Jingchao Lai, Weigen Yan","doi":"10.1007/s10955-024-03392-8","DOIUrl":null,"url":null,"abstract":"<div><p>Chang and Chen (J Stat Phys 131(4):631–650, 2008) and Chang et al. (J Stat Phys 126(3):649–667, 2007) present the number of dimer coverings and spanning trees on the Sierpinski gasket <span>\\(SG_b(n)\\)</span> at stage <i>n</i> with the side length <i>b</i> equal to two, three and four, respectively. In this paper, we obtain the exact closed formula of the number of dimer coverings and spanning trees on the silicate-type Sierpinski gasket <span>\\(SO_b(n)\\)</span> at stage <i>n</i> with the side length <span>\\(b=2,3,4\\)</span>.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 2","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10955-024-03392-8","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Chang and Chen (J Stat Phys 131(4):631–650, 2008) and Chang et al. (J Stat Phys 126(3):649–667, 2007) present the number of dimer coverings and spanning trees on the Sierpinski gasket \(SG_b(n)\) at stage n with the side length b equal to two, three and four, respectively. In this paper, we obtain the exact closed formula of the number of dimer coverings and spanning trees on the silicate-type Sierpinski gasket \(SO_b(n)\) at stage n with the side length \(b=2,3,4\).
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The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.
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