{"title":"Reduction of quad-equations consistent around a cuboctahedron I: Additive case","authors":"N. Joshi, N. Nakazono","doi":"10.1090/bproc/96","DOIUrl":null,"url":null,"abstract":"In this paper, we consider a reduction of a new system of partial difference equations, which was obtained in our previous paper (Joshi and Nakazono, arXiv:1906.06650) and shown to be consistent around a cuboctahedron. We show that this system reduces to $A_2^{(1)\\ast}$-type discrete Painleve equations by considering a periodic reduction of a three-dimensional lattice constructed from overlapping cuboctahedra.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"52 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the American Mathematical Society, Series B","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/bproc/96","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
In this paper, we consider a reduction of a new system of partial difference equations, which was obtained in our previous paper (Joshi and Nakazono, arXiv:1906.06650) and shown to be consistent around a cuboctahedron. We show that this system reduces to $A_2^{(1)\ast}$-type discrete Painleve equations by considering a periodic reduction of a three-dimensional lattice constructed from overlapping cuboctahedra.
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