C'edric Dion, Antonio Lei, Anwesh Ray, Daniel Vallières
{"title":"ON THE DISTRIBUTION OF IWASAWA INVARIANTS ASSOCIATED TO MULTIGRAPHS","authors":"C'edric Dion, Antonio Lei, Anwesh Ray, Daniel Vallières","doi":"10.1017/nmj.2023.18","DOIUrl":null,"url":null,"abstract":"\n\t <jats:p>Let <jats:inline-formula>\n\t <jats:alternatives>\n\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763023000181_inline1.png\" />\n\t\t<jats:tex-math>\n$\\ell $\n</jats:tex-math>\n\t </jats:alternatives>\n\t </jats:inline-formula> be a prime number. The Iwasawa theory of multigraphs is the systematic study of growth patterns in the number of spanning trees in abelian <jats:inline-formula>\n\t <jats:alternatives>\n\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763023000181_inline2.png\" />\n\t\t<jats:tex-math>\n$\\ell $\n</jats:tex-math>\n\t </jats:alternatives>\n\t </jats:inline-formula>-towers of multigraphs. In this context, growth patterns are realized by certain analogs of Iwasawa invariants, which depend on the prime <jats:inline-formula>\n\t <jats:alternatives>\n\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763023000181_inline3.png\" />\n\t\t<jats:tex-math>\n$\\ell $\n</jats:tex-math>\n\t </jats:alternatives>\n\t </jats:inline-formula> and the abelian <jats:inline-formula>\n\t <jats:alternatives>\n\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763023000181_inline4.png\" />\n\t\t<jats:tex-math>\n$\\ell $\n</jats:tex-math>\n\t </jats:alternatives>\n\t </jats:inline-formula>-tower of multigraphs. We formulate and study statistical questions about the behavior of the Iwasawa <jats:inline-formula>\n\t <jats:alternatives>\n\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763023000181_inline5.png\" />\n\t\t<jats:tex-math>\n$\\mu $\n</jats:tex-math>\n\t </jats:alternatives>\n\t </jats:inline-formula> and <jats:inline-formula>\n\t <jats:alternatives>\n\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763023000181_inline6.png\" />\n\t\t<jats:tex-math>\n$\\lambda $\n</jats:tex-math>\n\t </jats:alternatives>\n\t </jats:inline-formula> invariants.</jats:p>","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2022-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nagoya Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/nmj.2023.18","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
Abstract
Let
$\ell $
be a prime number. The Iwasawa theory of multigraphs is the systematic study of growth patterns in the number of spanning trees in abelian
$\ell $
-towers of multigraphs. In this context, growth patterns are realized by certain analogs of Iwasawa invariants, which depend on the prime
$\ell $
and the abelian
$\ell $
-tower of multigraphs. We formulate and study statistical questions about the behavior of the Iwasawa
$\mu $
and
$\lambda $
invariants.
期刊介绍:
The Nagoya Mathematical Journal is published quarterly. Since its formation in 1950 by a group led by Tadashi Nakayama, the journal has endeavoured to publish original research papers of the highest quality and of general interest, covering a broad range of pure mathematics. The journal is owned by Foundation Nagoya Mathematical Journal, which uses the proceeds from the journal to support mathematics worldwide.