A note on ranking functions
type: Item
instance of: scholarly article
title: A note on ranking functions
zbMATH Open document ID: 0646.06004
DOI: 10.1016/0012-365X(87)90180-4
author: Vojtěch Rödl
author: William T. Trotter
published in: Discrete Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The set L(n,r) of all possible results where n-competitors are matched in a series of r races is studied. The presented results are extensions of those obtained in \textit{W. J. Walker}'s paper ``Ranking functions and axioms for linear orders'' [reviewed above (see Zbl 0646.06003)]. Walker shows that L(n,r) is the intersection of the set of all consistent linear extensions. The concept of consistent dimension of L(n,r) is introduced as the least t for which the above result holds. Walker shows that the consistent dimension of L(n,r) equals the dimension of L(n,r) when \(r\leq 2\) and when \((n,r)=(4,3)\). The main result is that the consistent dimension of L(n,r) is much larger than its dimension.
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 06B05
zbMATH DE Number: 4053692
zbMATH Keywords: ranking function
zbMATH Keywords: results of races
zbMATH Keywords: consistent dimension
reviewed by: Frada Burstein
MaRDI profile type: Publication
cites work: Q3964626
cites work: Ranking functions and axioms for linear orders
full work available at URL: 0012-365x(87)90180-4
OpenAlex ID: W2171710204
description: scientific article; zbMATH DE number 4053692