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dc.contributor.authorEast, James
dc.contributor.authorKumar, Jitender
dc.contributor.authorMitchell, James D.
dc.contributor.authorWilson, Wilf A.
dc.identifier.citationEast , J , Kumar , J , Mitchell , J D & Wilson , W A 2018 , ' Maximal subsemigroups of finite transformation and diagram monoids ' , Journal of Algebra , vol. 504 , pp. 176-216 .
dc.identifier.otherRIS: urn:51F957BCA043BD3D49090344FAA7E948
dc.identifier.otherORCID: /0000-0002-5489-1617/work/73700794
dc.identifier.otherORCID: /0000-0002-3382-9603/work/85855347
dc.descriptionThe first author gratefully acknowledges the support of the Glasgow Learning, Teaching, and Research Fund in partially funding his visit to the third author in July, 2014. The second author wishes to acknowledge the support of research initiation grant [0076|2016] provided by BITS Pilani, Pilani. The fourth author wishes to acknowledge the support of his Carnegie Ph.D. Scholarship from the Carnegie Trust for the Universities of Scotland.en
dc.description.abstractWe describe and count the maximal subsemigroups of many well-known transformation monoids, and diagram monoids, using a new unified framework that allows the treatment of several classes of monoids simultaneously. The problem of determining the maximal subsemigroups of a finite monoid of transformations has been extensively studied in the literature. To our knowledge, every existing result in the literature is a special case of the approach we present. In particular, our technique can be used to determine the maximal subsemigroups of the full spectrum of monoids of order- or orientation-preserving transformations and partial permutations considered by I. Dimitrova, V. H. Fernandes, and co-authors. We only present details for the transformation monoids whose maximal subsemigroups were not previously known; and for certain diagram monoids, such as the partition, Brauer, Jones, and Motzkin monoids. The technique we present is based on a specialised version of an algorithm for determining the maximal subsemigroups of any finite semigroup, developed by the third and fourth authors, and available in the Semigroups package for GAP, an open source computer algebra system. This allows us to concisely present the descriptions of the maximal subsemigroups, and to clearly see their common features.
dc.relation.ispartofJournal of Algebraen
dc.subjectMaximal subsemigroupsen
dc.subjectTransformation semigroupen
dc.subjectDiagram monoiden
dc.subjectPermutation groupsen
dc.subjectMaximal subgroupsen
dc.subjectMaximal independent seten
dc.subjectPartition monoiden
dc.subjectQA Mathematicsen
dc.titleMaximal subsemigroups of finite transformation and diagram monoidsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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