Related papers: Cofinality of Regular Tournaments
In this article we introduce and study a class of finite groups for which the orders of normal subgroups satisfy a certain inequality. It is closely connected to some well-known arithmetic classes of natural numbers.
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…
We study the problem of computing all Nash equilibria of a subclass of finite normal form games. With algebraic characterization of the games, we present a method for computing all its Nash equilibria. Further, we present a method for…
In this note we introduce and characterize a class of finite groups for which the element orders satisfy a certain inequality. This is contained in some well-known classes of finite groups.
In this paper we present a new proof of a proposition presented in the article: Complexes of tournaments, directionality filtrations and persistent homology. This paper is part of Joaqu\'in Casta\~neda's undergraduate thesis.
Using generating functions, we enumerate regular semisimple conjugacy classes in the finite classical groups. For the general linear, unitary, and symplectic groups this gives a different approach to known results; for the special…
We prove that every finitary polynomial endofunctor of a category $C$ has a final coalgebra if $C$ is locally Cartesian closed, has finite disjoint coproducts and a natural number object. More generally, we prove that the category of…
We study the effects of randomness on competitions based on an elementary random process in which there is a finite probability that a weaker team upsets a stronger team. We apply this model to sports leagues and sports tournaments, and…
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…
We look at spaces of infinite-by-infinite matrices, and consider closed subsets that are stable under simultaneous row and column operations. We prove that up to symmetry, any of these closed subsets is defined by finitely many equations.
The purpose of this note is to start the systematic analysis of cofinal types of topological groups.
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…
We prove that every profinite group in a certain class with a rational probabilistic zeta function has only finitely many maximal subgroups.
Classes of algebraic structures that are defined by equational laws are called varieties or equational classes. A variety is finitely generated if it is defined by the laws that hold in some fixed finite algebra. We show that every…
In the run-up to any major sports tournament, winning probabilities of participants are publicized for engagement and betting purposes. These are generally based on simulating the tournament tens of thousands of times by sampling from…
We provide a complete classification of the possible cofinal structures of the families of precompact (totally bounded) sets in general metric spaces, and compact sets in general complete metric spaces. Using this classification, we…
We establish the density of the partial regularity result in the class of continuous viscosity solutions. Given a fully nonlinear equation, we prove the existence of a sequence entitled to the partial regularity result, approximating its…
We prove that for every $n\geq 2$ the class of all finite $n$-partite tournaments (orientations of complete $n$-partite graphs) has the extension property for partial automorphisms, that is, for every finite $n$-partite tournament $G$ there…
The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here "compute" means to find a presentation in terms of generators and relations, and involves only the…
Motivated by known results for finite tournaments, we define and study the score functions of tournament kernels and the degree distributions of tournament limits. Our main theorem completely characterises those distributions that appear as…