Work

Coxeter Tournaments

Year: 2026

Type: article

Abstract: 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.

Source: Annals of Combinatorics

DOI: 10.1007/s00026-026-00824-y

Authors: Brett Kolesnik, Mario Sanchez

Institutions: University of Warwick, Cornell University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: National Science Foundation