dc.contributor.author | Carvalho, Catarina | |
dc.contributor.author | Martin, Barnaby | |
dc.date.accessioned | 2022-07-06T14:15:01Z | |
dc.date.available | 2022-07-06T14:15:01Z | |
dc.date.issued | 2021-11-10 | |
dc.identifier.citation | Carvalho , C & Martin , B 2021 , ' The lattice and semigroup structure of multipermutations ' , International Journal of Algebra and Computation , vol. 32 , no. 2 . https://doi.org/10.1142/S0218196722500096 | |
dc.identifier.issn | 0218-1967 | |
dc.identifier.other | ORCID: /0000-0002-4648-7016/work/115596727 | |
dc.identifier.uri | http://hdl.handle.net/2299/25601 | |
dc.description | Publisher Copyright: © 2021 World Scientific Publishing Company. | |
dc.description.abstract | We study the algebraic properties of binary relations whose underlying digraph is smooth, that is, has no source or sink. Such objects have been studied as surjective hyper-operations (shops) on the corresponding vertex set, and as binary relations that are defined everywhere and whose inverse is also defined everywhere. In the latter formulation, they have been called multipermutations. We study the lattice structure of sets (monoids) of multipermutations over an n-element domain. Through a Galois connection, these monoids form the algebraic counterparts to sets of relations closed under definability in positive first-order logic without equality. We show one side of this Galois connection, and give a simple dichotomy theorem for the evaluation problem of positive first-order logic without equality on the class of structures whose preserving multipermutations form a monoid closed under inverse. These problems turn out either to be in Logspaceor to be Pspace-complete. We go on to study the monoid of all multipermutations on an n-element domain, under usual composition of relations. We characterize its Green relations, regular elements and show that it does not admit a generating set that is polynomial on n. | en |
dc.format.extent | 478266 | |
dc.language.iso | eng | |
dc.relation.ispartof | International Journal of Algebra and Computation | |
dc.subject | Galois connection | |
dc.subject | binary relation | |
dc.subject | model-checking problem | |
dc.subject | Mathematics(all) | |
dc.title | The lattice and semigroup structure of multipermutations | en |
dc.contributor.institution | School of Physics, Engineering & Computer Science | |
dc.contributor.institution | Mathematics and Theoretical Physics | |
dc.contributor.institution | Centre for Computer Science and Informatics Research | |
dc.contributor.institution | Department of Physics, Astronomy and Mathematics | |
dc.description.status | Peer reviewed | |
dc.identifier.url | http://www.scopus.com/inward/record.url?scp=85114929122&partnerID=8YFLogxK | |
rioxxterms.versionofrecord | 10.1142/S0218196722500096 | |
rioxxterms.type | Journal Article/Review | |
herts.preservation.rarelyaccessed | true | |