.png){kind=icon}
.png){kind=icon}
Return
Coxeter Tournaments
.png){kind=icon}
PRE
AI
DOI：10.1007/s00026-026-00824-y.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
We describe the Coxeter permutahedra, recently studied by Ardila, Castillo, Eur and Postnikov, in terms of random Coxeter tournaments, which involve cooperative and solitaire games, as well as the usual competitive games in graph tournaments. In this way, we establish a Coxeter version of Moon's theorem on random tournaments. We present a geometric proof by the Mirsky-Thompson generalized Birkhoff's theorem, a probabilistic proof by Strassen's coupling theorem, and an algorithmic proof by a Coxeter analogue of the Havel-Hakimi algorithm. These proofs have interpretations in terms of players choosing competitors/collaborators with respect to relative weakness/strength. We also introduce a natural Coxeter analogue of the Bradley-Terry model, from the statistical theory of paired comparisons.
Keywords:
Bradley-Terry model
Coxeter permutahedra
Digraph
Havel-Hakimi algorithm
Majorization
Paired comparisons
Permutahedron
Root system
Score sequence
Signed graph
Submodular function
Tournament
Zonotope
Journal
A
IF:
0.7
Papers:
45
Citations:
0