An n × n complex matrix A is h-pseudo-tournament if A + A∗ = hh∗ − I, where h is a complex, non-zero column vector. The class of h-pseudo-tournament matrices is a generalization of the well studied tournament-like matrices: h-hypertournament matrices, generalized tournament matrices and tournament matrices. In this paper we derive new spectral properties of an h-pseudo-tournament matrix. When t...

We consider the manipulability of tournament rules for round-robin tournaments of n competitors. Specifically, n competitors are competing for a prize, and a tournament rule r maps the result of all (n 2 ) pairwise matches (called a tournament, T ) to a distribution over winners. Rule r is Condorcet-consistent if whenever i wins all n− 1 of her matches, r selects i with probability 1. We consid...

A directed graph where there is exactly one edge between every pair of vertices is called a tournament. Finding the “best” set of vertices of a tournament is a well studied problem in social choice theory. A tournament solution takes a tournament as input and outputs a subset of vertices of the input tournament. However, in many applications, for example, choosing the best set of drugs from a g...

Tournament selection performs tournaments by first sampling individuals uniformly at random from the population and then selecting the best of the sample for some genetic operation. This sampling process needs to be repeated many times when creating a new generation. However, even upon iteration, it may happen not to sample some of the individuals in the population. These individuals can theref...

Competitiveness of sporting contests is key to attract fan interest. However, limited research compared levels competitiveness in men’s and women’s sports. This study focuses on the evolution intra-match competitive balance (IMCB) intensity (IMCI) UEFA Men’s Women’s Champions League (UMCL UWCL). Data were initially collected for 3299 games over 2001–2019 (2314 UMCL; 985 UWCL) analyse within bet...

We explore the behavior of losers of promotion tournaments after the tournament is concluded. We do so through the use of an experiment in which we vary the design of the promotion tournament to determine how tournament design affects post tournament effort. We provide a theoretical model demonstrating two possible effects from the tournaments which are strategic sabotage and the possibility th...

In a recent paper, we showed that every sufficiently large regular digraph G on n vertices whose degree is linear in n and which is a robust outexpander has a decomposition into edge-disjoint Hamilton cycles. The main consequence of this theorem is that every regular tournament on n vertices can be decomposed into (n − 1)/2 edge-disjoint Hamilton cycles, whenever n is sufficiently large. This v...

Optimal seeding in balanced knockout tournaments has only been studied in very limited settings, for example, maximizing predictive power for up to 8 players using only the relative ranking of the players (ordinal information). We dramatically broaden the scope of the analysis along several dimensions. First, we propose a heuristic algorithm that makes use of available cardinal information and ...

We answer a question of P. Cameron’s by giving examples of 2א0 many non-isomorphic acyclic orientations of the infinite random graph with a topological ordering that do not have the pigeonhole property. Our examples also embed each countable linear ordering. A graph is n-existentially closed or n-e.c. if for each n-subset S of vertices, and each subset T of S (possibly empty), there is a vertex...