Ranking functions and axioms for linear orders
type: Item
instance of: scholarly article
title: Ranking functions and axioms for linear orders
zbMATH Open document ID: 0646.06003
DOI: 10.1016/0012-365X(87)90179-8
author: W. J. Walker
published in: Discrete Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The problem of ranking n competitors by their results after participation in r races is studied. For fixed n and r there exist the set of all results denoted \(L(n,r)\). \(L(n,r)\) is considered a distributive lattice with the partial order P on it. The isomorphism between \(L(p,q)\) and \(L(q+1,p-1)\) is shown. The notion of dimension of this set is considered. Two axioms are given for the set of results and the notion of dimension is investigated for linear orders with respect to these axioms. For the particular case \((n=0\), \(r\geq 2)\) it is proved that \(L(3,r)\) has dimension \(D(n,r)=2\). A more common theorem is proved by \textit{W. T. Trotter} and \textit{V. Rödl} [reviewed below (see Zbl 0646.06004)].
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 06B05
zbMATH DE Number: 4053691
zbMATH Keywords: results of races
zbMATH Keywords: dimension
Wikidata QID: Q114686140
reviewed by: Frada Burstein
MaRDI profile type: Publication
cites work: Q4146776
cites work: Q4748185
cites work: Partially Ordered Sets
cites work: Q3964626
cites work: The enumeration and bifurcations of ranking functions
cites work: Rankings and Ranking Functions
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description: scientific article; zbMATH DE number 4053691