The Geometry of Random Tournaments

被引：0
作者：
Brett Kolesnik
Mario Sanchez
机构：
[1] University of Oxford,Department of Statistics
[2] Cornell University,Department of Mathematics
来源：
Discrete & Computational Geometry | 2024年 / 71卷
关键词：
Digraph; Mixed subdivision; Permutahedra; Tournament; Zonotope; 05C80; 05C85; 49M25; 60F10; 65N22; 68W40;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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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页码：1343 / 1351
页数：8
相关论文
共 28 条
[1]  
Aigner M(1984)Uses of the diagram lattice Mitt. Math. Sem. Giessen 163 61-77
[2]  
Aldous DJ(2022)To stay discovered: on tournament mean score sequences and the Bradley–Terry model Stoch. Process. Appl. 150 844-852
[3]  
Kolesnik B(1968)A new proof of a theorem by H.G. Landau on tournament matrices J. Combin. Theory 5 289-292
[4]  
Brauer A(2015)Tournaments associated with multigraphs and a theorem of Hakimi Discrete Math. 338 229-235
[5]  
Gentry IC(2001)Landau’s inequalities for tournament scores and a short proof of a theorem on transitive sub-tournaments J. Graph Theory 38 244-254
[6]  
Shaw K(1987)A tournament result deduced from harems Elem. Math. 42 153-156
[7]  
Brualdi RA(2014)On linear programming duality and Landau’s characterization of tournament scores Acta Univ. Sapientiae Inform. 6 21-32
[8]  
Fritscher E(1960)Zero-one matrices with zero trace Pac. J. Math. 10 831-836
[9]  
Brualdi RA(1965)Upsets in round robin tournaments Can. J. Math. 17 957-969
[10]  
Shen J(2017)On degree sequences of undirected, directed, and bidirected graphs Eur. J. Combin. 64 113-124
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