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Properties of congruences of twisted partition monoids and their lattices
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dc.contributor.author | East, James | |
dc.contributor.author | Ruskuc, Nik | |
dc.date.accessioned | 2021-11-09T13:30:11Z | |
dc.date.available | 2021-11-09T13:30:11Z | |
dc.date.issued | 2022-07 | |
dc.identifier | 276617343 | |
dc.identifier | 77842807-e613-4a4f-8d15-b69ae2ee6fa6 | |
dc.identifier | 000769177100001 | |
dc.identifier | 85126269817 | |
dc.identifier.citation | East , J & Ruskuc , N 2022 , ' Properties of congruences of twisted partition monoids and their lattices ' , Journal of the London Mathematical Society , vol. 106 , no. 1 , pp. 311-357 . https://doi.org/10.1112/jlms.12574 | en |
dc.identifier.issn | 0024-6107 | |
dc.identifier.other | ORCID: /0000-0003-2415-9334/work/110131502 | |
dc.identifier.uri | https://hdl.handle.net/10023/24300 | |
dc.description | Funding: The first author is supported by ARC Future Fellowship FT190100632. The second author is supported by EPSRC grant EP/S020616/1. | en |
dc.description.abstract | We build on the recent characterisation of congruences on the infinite twisted partition monoids PΦn and their finite d-twisted homomorphic images PΦn,d, and investigate their algebraic and order-theoretic properties. We prove that each congruence of PΦn is (finitely) generated by at most ⌈5n/2⌉ pairs, and we characterise the principal ones. We also prove that the congruence lattice Cong(PΦn) is not modular (or distributive); it has no infinite ascending chains, but it does have infinite descending chains and infinite antichains. By way of contrast, the lattice Cong(PΦn,d) is modular but still not distributive for d>0, while Cong(PΦn,0) is distributive. We also calculate the number of congruences of PΦn,d, showing that the array (|Cong(PΦn,d)|)n,d≥0 has a rational generating function, and that for a fixed n or d, |Cong(PΦn,d)| is a polynomial in d or n≥4, respectively. | |
dc.format.extent | 3541250 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of the London Mathematical Society | en |
dc.subject | Partition monoid | en |
dc.subject | Twisted partition monoid | en |
dc.subject | Congruence | en |
dc.subject | Finitely generated congruence | en |
dc.subject | Principal congruence | en |
dc.subject | Congruence lattice | en |
dc.subject | Modular lattice | en |
dc.subject | Distributive lattice | en |
dc.subject | Enumeration | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Properties of congruences of twisted partition monoids and their lattices | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | https://doi.org/10.1112/jlms.12574 | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | https://arxiv.org/abs/2010.09288 | en |
dc.identifier.grantnumber | EP/S020616/1 | en |
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