{"title":"The Geometry of Random Tournaments","authors":"Mario Sanchez, Brett Kolesnik","doi":"10.1007/s00454-023-00571-4","DOIUrl":null,"url":null,"abstract":"Abstract A tournament is an orientation of a graph. Each edge is a match, directed towards the winner. The score sequence lists the number of wins by each team. In this article, by interpreting score sequences geometrically, we generalize and extend classical theorems of Landau (Bull. Math. Biophys. 15 , 143–148 (1953)) and Moon (Pac. J. Math. 13 , 1343–1345 (1963)), via the theory of zonotopal tilings.","PeriodicalId":356162,"journal":{"name":"Discrete and Computational Geometry","volume":"63 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete and Computational Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00454-023-00571-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract A tournament is an orientation of a graph. Each edge is a match, directed towards the winner. The score sequence lists the number of wins by each team. In this article, by interpreting score sequences geometrically, we generalize and extend classical theorems of Landau (Bull. Math. Biophys. 15 , 143–148 (1953)) and Moon (Pac. J. Math. 13 , 1343–1345 (1963)), via the theory of zonotopal tilings.
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