Related papers: Tournament limits: Degree distributions, score fun…
The theory of tournament limits and tournament kernels (often called graphons) is developed by extending common notions for finite tournaments to this setting; in particular we study transitivity and irreducibility of limits and kernels. We…
We consider a general class of round-robin tournament models of equally strong players. In these models, each of the $n$ players competes against every other player exactly once. For each match between two players, the outcome is a value…
Based on known methods for computing the number of distinct score sequences for $n$-vertex tournaments, we develop algorithms for computing the number of distinct score sequences for self-complementary tournaments, strong tournaments, and…
The converse of a tournament is obtained by reversing all arcs. If a tournament is isomorphic to its converse, it is called self--converse. Eplett provided a necessary and sufficient condition for a sequence of integers to be realisable as…
The score sequence of a tournament is the sequence of the out-degrees of its vertices arranged in nondecreasing order. The problem of counting score sequences of a tournament with $n$ vertices is more than 100 years old (MacMahon 1920). In…
Every sport needs rules. Tournament design refers to the rules that determine how a tournament, a series of games between a number of competitors, is organized. This study aims to provide an overview of the tournament design literature from…
We study statistics of the knockout tournament, where only the winner of a fixture progresses to the next. We assign a real number called competitiveness to each contestant and find that the resulting distribution of prize money follows a…
A tournament on 8 or more vertices may be intrinsically linked as a directed graph. We begin the classification of intrinsically linked tournaments by examining their score sequences. While many distinct tournaments may have the same score…
In the paper, we define a new parameter for tournaments called degreewidth which can be seen as a measure of how far is the tournament from being acyclic. The degreewidth of a tournament $T$ denoted by $\Delta(T)$ is the minimum value $k$…
In many applications of machine learning, a large number of variables are considered. Motivated by machine learning of interacting particle systems, we consider the situation when the number of input variables goes to infinity. First, we…
In this paper we bring a novel approach to the theory of tournament rankings. We combine two different theories that are widely used to establish rankings of populations after a given tournament. First, we use the statistical approach of…
There seems to be an upper limit to predicting the outcome of matches in (semi-)professional sports. Recent work has proposed that this is due to chance and attempts have been made to simulate the distribution of win percentages to identify…
We form a "map of tournaments" by adapting the map framework from the world of elections. By a tournament we mean a complete directed graph where the nodes are the players and an edge points from a winner of a game to the loser (with no…
In this thesis we prove a variety of theorems on tournaments. A \emph{prime} tournament is a tournament $G$ such that there is no $X \subseteq V(G)$, $1 < |X| < |V(G)|$, such that for every vertex $v \in V(G) \minus X$, either $v \ra x$ for…
In a classical chess round-robin tournament, each of $n$ players wins, draws, or loses a game against each of the other $n-1$ players. A win rewards a player with 1 points, a draw with 1/2 point, and a loss with 0 points. We are interested…
The use of second order boundary kernels for distribution function estimation was recently addressed in the literature (C. Tenreiro, 2013, Boundary kernels for distribution function estimation, REVSTAT-Statistical Journal, 11, 169-190). In…
We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a…
A random walk-like model is considered to discuss statistical aspects of tournaments. The model is applied to soccer leagues with emphasis on the scores. This competitive system was computationally simulated and the results are compared…
We completely characterize the class of univariate distributions allowing for a Stein kernel and illustrate our result by means of some concrete distributions. Moreover, we apply our findings to prove a quantitative version of the central…
Say you and some friends decide to make brackets for March Madness and are told how each of your brackets scored. The question we ask is: when can you determine how the actual tournament went given your scores? We determine the exact…