{"title":"On the number of faces of the Gelfand–Zetlin polytope","authors":"E. Melikhova","doi":"10.1090/spmj/1714","DOIUrl":null,"url":null,"abstract":"The combinatorics of the Gelfand–Zetlin polytope is studied. Geometric properties of a linear projection of this polytope onto a cube are employed to derive a recurrence relation for the \n\n \n f\n f\n \n\n-polynomial of the polytope. This recurrence relation is applied to finding the \n\n \n f\n f\n \n\n-polynomials and \n\n \n h\n h\n \n\n-polynomials for one-parameter families of Gelfand–Zetlin polytopes of simplest types.","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"St Petersburg Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/spmj/1714","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The combinatorics of the Gelfand–Zetlin polytope is studied. Geometric properties of a linear projection of this polytope onto a cube are employed to derive a recurrence relation for the
f
f
-polynomial of the polytope. This recurrence relation is applied to finding the
f
f
-polynomials and
h
h
-polynomials for one-parameter families of Gelfand–Zetlin polytopes of simplest types.
期刊介绍：
This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.
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