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Permutation monoids and MB-homogeneity for graphs and relational structures
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dc.contributor.author | Coleman, Thomas D. H. | |
dc.contributor.author | Gray, Robert | |
dc.contributor.author | Evans, David | |
dc.date.accessioned | 2020-03-05T00:31:57Z | |
dc.date.available | 2020-03-05T00:31:57Z | |
dc.date.issued | 2019-05 | |
dc.identifier | 257559188 | |
dc.identifier | 0710dda2-1109-483c-ab3e-f4069872a878 | |
dc.identifier | 85062405199 | |
dc.identifier | 000465187100012 | |
dc.identifier.citation | Coleman , 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.2019.02.005 | en |
dc.identifier.issn | 0195-6698 | |
dc.identifier.other | ORCID: /0000-0003-2012-4919/work/64698154 | |
dc.identifier.uri | https://hdl.handle.net/10023/19599 | |
dc.description | This 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.abstract | In 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.extent | 420807 | |
dc.language.iso | eng | |
dc.relation.ispartof | European Journal of Combinatorics | en |
dc.subject | Biomorphisms | en |
dc.subject | MB-homogeneous | en |
dc.subject | Cancellative monoids | en |
dc.subject | Permutation monoids | en |
dc.subject | Oligomorphic transformation monoids | en |
dc.subject | Homomorphism-homogeneous structures | en |
dc.subject | Infinite graph theory | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Permutation monoids and MB-homogeneity for graphs and relational structures | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | https://doi.org/10.1016/j.ejc.2019.02.005 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2020-03-05 |
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