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dc.contributor.authorColeman, Thomas D. H.
dc.contributor.authorGray, Robert
dc.contributor.authorEvans, David
dc.date.accessioned2020-03-05T00:31:57Z
dc.date.available2020-03-05T00:31:57Z
dc.date.issued2019-05
dc.identifier257559188
dc.identifier0710dda2-1109-483c-ab3e-f4069872a878
dc.identifier85062405199
dc.identifier000465187100012
dc.identifier.citationColeman , T D H , Gray , R & Evans , D 2019 , ' Permutation monoids and MB-homogeneity for graphs and relational structures ' , European Journal of Combinatorics , vol. 78 , pp. 163-189 . https://doi.org/10.1016/j.ejc.2019.02.005en
dc.identifier.issn0195-6698
dc.identifier.otherORCID: /0000-0003-2012-4919/work/64698154
dc.identifier.urihttps://hdl.handle.net/10023/19599
dc.descriptionThis work was supported by the EPSRC (United Kingdom) grant EP/N033353/1 ‘Special inverse monoids: subgroups, structure, geometry, rewriting systems and the word problem’.en
dc.description.abstractIn this paper we investigate the connection between infinite permutation monoids and bimorphism monoids of first-order structures. Taking our lead from the study of automorphism groups of structures as infinite permutation groups and the more recent developments in the field of homomorphism-homogeneous structures, we establish a series of results that underline this connection. Of particular interest is the idea of MB-homogeneity; a relational structure M is MB-homogeneous if every monomorphism between finite substructures of M extends to a bimorphism of M. The results in question include a characterisation of closed permutation monoids, a Fraïssé-like theorem for MB-homogeneous structures, and the construction of 2N0 pairwise non-isomorphic countable MB-homogeneous graphs. We prove that any finite group arises as the automorphism group of some MB-homogeneous graph and use this to construct oligomorphic permutation monoids with any given finite group of units. We also consider MB-homogeneity for various well-known examples of homogeneous structures and in particular give a complete classification of countable homogeneous undirected graphs that are also MB-homogeneous.
dc.format.extent420807
dc.language.isoeng
dc.relation.ispartofEuropean Journal of Combinatoricsen
dc.subjectBiomorphismsen
dc.subjectMB-homogeneousen
dc.subjectCancellative monoidsen
dc.subjectPermutation monoidsen
dc.subjectOligomorphic transformation monoidsen
dc.subjectHomomorphism-homogeneous structuresen
dc.subjectInfinite graph theoryen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titlePermutation monoids and MB-homogeneity for graphs and relational structuresen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doi10.1016/j.ejc.2019.02.005
dc.description.statusPeer revieweden
dc.date.embargoedUntil2020-03-05


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