Combinatorial aspects of relations
type: Item
instance of: scholarly article
title: Combinatorial aspects of relations
zbMATH Open document ID: 0549.20059
DOI: 10.1007/BF01182249
author: Stephen D. Comer
published in: Algebra Universalis
publication date: 1984-01-01T00:00:00Z
review text: A multivalued group-like system called polygroup (a special type of multigroup in the sense of \textit{M. Dresher} and \textit{Ø. Ore} [Am. J. Math. 60, 705-733 (1938; Zbl 0019.10701)] is introduced. Polygroups can be characterized as the atomic structures (under composition and reverse) of complete atomic integral relation algebras (see \textit{B. Jónsson} and \textit{A. Tarski} [ibid. 74, 127-162 (1952; Zbl 0049.15801)]. Due to this, there is a correspondence between certain properties of IRA's (such as different kinds of representability) and those of polygroups. Also, information can be obtained about automorphism groups of colour schemes (colourings of the edges of complete graphs, subject to some conditions) from the knowledge of polygroups attached to them (so called chromatic polygroups). The last two theorems give some approach to problems concerning the orbits of stabilizers of the elements in transitive permutation groups by ways of polygroups.
Mathematics Subject Classification ID: 20N99
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 08A02
Mathematics Subject Classification ID: 20B20
zbMATH DE Number: 3875564
zbMATH Keywords: multivalued group-like system
zbMATH Keywords: atomic structures
zbMATH Keywords: complete atomic integral relation algebras
zbMATH Keywords: automorphism groups of colour schemes
zbMATH Keywords: complete graphs
zbMATH Keywords: chromatic polygroups
zbMATH Keywords: orbits of stabilizers
zbMATH Keywords: transitive permutation groups
MaRDI profile type: Publication
cites work: Q4770409
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full work available at URL: https://doi.org/10.1007/bf01182249
OpenAlex ID: W2035863510
description: scientific article; zbMATH DE number 3875564