{"title":"关于整数凸多边形的顶点数","authors":"H. Ravelonirina, J. J. Rakoto","doi":"10.37418/amsj.12.6.4","DOIUrl":null,"url":null,"abstract":"The aim of this paper is to propose a polynomial that we call ''characteristic polynomial'' of an integer convex polytope of dimension $d$ $(d\\geq1)$. This polynomial makes it possible to count the number of vertices of an integer convex polytope without using the Schl\\\"afli symbol. We give after that the algebraic characteristics of this polynomial.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"122 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ON THE NUMBER OF VERTICES OF INTEGER CONVEX POLYTOPES\",\"authors\":\"H. Ravelonirina, J. J. Rakoto\",\"doi\":\"10.37418/amsj.12.6.4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The aim of this paper is to propose a polynomial that we call ''characteristic polynomial'' of an integer convex polytope of dimension $d$ $(d\\\\geq1)$. This polynomial makes it possible to count the number of vertices of an integer convex polytope without using the Schl\\\\\\\"afli symbol. We give after that the algebraic characteristics of this polynomial.\",\"PeriodicalId\":231117,\"journal\":{\"name\":\"Advances in Mathematics: Scientific Journal\",\"volume\":\"122 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-06-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Mathematics: Scientific Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37418/amsj.12.6.4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics: Scientific Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37418/amsj.12.6.4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
ON THE NUMBER OF VERTICES OF INTEGER CONVEX POLYTOPES
The aim of this paper is to propose a polynomial that we call ''characteristic polynomial'' of an integer convex polytope of dimension $d$ $(d\geq1)$. This polynomial makes it possible to count the number of vertices of an integer convex polytope without using the Schl\"afli symbol. We give after that the algebraic characteristics of this polynomial.
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