2019/11/20 by Yuming Zhang, Xinmin Hou, Zhang, Yuming +1
Computer Science · Economics, Econometrics and Finance · #05C20 #Artificial Intelligence in Games #Combinatorics (math.CO) #Data Mining Algorithms and Applications #FOS: Mathematics #Sports Analytics and Performance
paper · pdf · doi:10.48550/arxiv.1911.08653
openalex publication_date 2019/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let T be a tournament with nondecreasing score sequence R and A be its tournament matrix. An upset of T corresponds to an entry above the main diagonal of A. Given a feasible score sequence R, Fulkerson~(1965) gave a simple recursive construction for a tournament with score sequence R and the minimum number of upsets, and Hacioglu et al. (2019) provided a construction for all of such tournament matrices. Let Umin(R) denote the set of tournament matrices with score sequence R that have minimum number of upsets. Brauldi and Li~(1983) characterized the strong score sequences R (R is strong if a tournament T with score sequence R is strongly connected) with |Umin(R)|=1. In this article, we characterize all feasible score sequences R with |Umin(R)|=1 and give an explicit formula for the number of the feasible score sequences R with |Umin(R)|=1.