Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · math/0601053

Ranking Participants in Tournaments by means of Rating Functions

M. Brozos-Vazquez·M. A. Campo-Cabana·J. C. Diaz-Ramos·J. Gonzalez-Diaz
View original source ↗Read source document ↗Export metadata ↓

Abstract

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 paired comparison analysis to define the performance of a player in a natural way. Then, we determine a ranking (and rating) of the players in the given tournament. Finally, we show, among other properties, that the new ranking method is the unique one satisfying a natural consistency requirement.

Explore related subjects

math.GMmath.CO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

M. Brozos-Vazquez, M. A. Campo-Cabana, J. C. Diaz-Ramos, J. Gonzalez-Diaz. 2006-12-02. Ranking Participants in Tournaments by means of Rating Functions. https://arxiv.org/abs/math/0601053

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The Collatz Conjecture & Non-Archimedean Spectral Theory -- Part II -- $\left(p,q\right)$-Adic Fourier Analysis and Wiener's Tauberian Theorem

This paper gives an overview of $\left(p,q\right)$-adic Fourier theory - the Fourier theory of functions from the $p$-adic numbers to the $q$-adic numbers, where $p$ and $q$ are distinct primes - which we then use to prove a novel $\left(p,q\right)$-adic generalization of Norbert Wiener's celebrated Tauberian Theorem. Letting $K$ be a metrically complete, algebraically closed local field of residue characteristic $q$, letting $C\left(\mathbb{Z}_{p},K\right)$ be the Banach space of continuous functions $\mathbb{Z}_{p}\rightarrow K$, and letting $dμ$ be a $\left(p,q\right)$-adic measure (a continuous linear functional $C\left(\mathbb{Z}_{p},K\right)\rightarrow K)$, the $\left(p,q\right)$-adic Wiener Tauberian Theorem (WTT) we prove establishes that the density of the span of translates of $dμ$'s Fourier-Stieltjes Transform implies the non-vanishing of the Radon-Nikodym derivative of $dμ$ at all points in $\mathbb{Z}_{p}$ where the derivative exists in $K$.

math.GM↗
arXiv2026

Indefinite integrals of Bessel and Struve functions with half-integer indices, and incomplete gamma functions with integer indices, all multiplied by $Exp(-ax^{2})$ and divided by powers

Indefinite integrals are found for 63 half-integer Bessel and Struve functions, and incomplete gamma functions with integer indices, each multiplied by $Exp(-ax^{2})$ and divided by powers. A series solution is given for the individual terms (of any inverse power) in such functions, split into even and odd portions. Eight integrals are given involving these series. Three infinite sets of auxiliary integrals are also given.

math.GM↗