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Generating the full transformation semigroup using order preserving mappings

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dc.contributor.authorHiggins, PM
dc.contributor.authorMitchell, James David
dc.contributor.authorRuskuc, Nikola
dc.date.accessioned2010-12-01T10:42:48Z
dc.date.available2010-12-01T10:42:48Z
dc.date.issued2003-09
dc.identifier.citationHiggins , PM , Mitchell , J D & Ruskuc , N 2003 , ' Generating the full transformation semigroup using order preserving mappings ' , Glasgow Mathematical Journal , vol. 45 , no. 3 , pp. 557-566 . https://doi.org/10.1017/S0017089503001460en
dc.identifier.issn0017-0895
dc.identifier.otherPURE: 230874
dc.identifier.otherPURE UUID: 83e2237f-6c79-405f-a985-15f1d63f6b7b
dc.identifier.otherWOS: 000185755000013
dc.identifier.otherScopus: 0141640991
dc.identifier.otherORCID: /0000-0002-5489-1617/work/73700828
dc.identifier.otherORCID: /0000-0003-2415-9334/work/73702081
dc.identifier.urihttp://hdl.handle.net/10023/1553
dc.description.abstractFor a linearly ordered set X we consider the relative rank of the semigroup of all order preserving mappings O-X on X modulo the full transformation semigroup Ex. In other words, we ask what is the smallest cardinality of a set A of mappings such that <O-X boolean OR A> = T-X. When X is countably infinite or well-ordered (of arbitrary cardinality) we show that this number is one, while when X = R (the set of real numbers) it is uncountable.
dc.format.extent10
dc.language.isoeng
dc.relation.ispartofGlasgow Mathematical Journalen
dc.rights(c)2003 Glasgow Mathematical Journal Trusten
dc.subjectRanksen
dc.subjectQA Mathematicsen
dc.subject.lccQAen
dc.titleGenerating the full transformation semigroup using order preserving mappingsen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. School of Mathematics and Statisticsen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doihttps://doi.org/10.1017/S0017089503001460
dc.description.statusPeer revieweden
dc.identifier.urlhttp://www.scopus.com/inward/record.url?scp=0141640991&partnerID=8YFLogxKen


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