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dc.contributor.authorEast, James
dc.contributor.authorRuskuc, Nik
dc.date.accessioned2022-11-18T00:39:49Z
dc.date.available2022-11-18T00:39:49Z
dc.date.issued2021-11-18
dc.identifier276340272
dc.identifiercb393d85-9726-40bc-939f-e192b71879a1
dc.identifier85119523940
dc.identifier000792762400014
dc.identifier.citationEast , J & Ruskuc , N 2021 , ' Classification of congruences of twisted partition monoids ' , Advances in Mathematics , vol. In Press . https://doi.org/10.1016/j.aim.2021.108097en
dc.identifier.issn0001-8708
dc.identifier.otherORCID: /0000-0003-2415-9334/work/104252282
dc.identifier.urihttps://hdl.handle.net/10023/26434
dc.descriptionFunding: The first author is supported by ARC Future Fellowship FT190100632. The second author is supported by EPSRC grant EP/S020616/1.en
dc.description.abstractThe twisted partition monoid PΦn is an infinite monoid obtained from the classical finite partition monoid Pn by taking into account the number of floating components when multiplying partitions. The main result of this paper is a complete description of the congruences on PΦn. The succinct encoding of a congruence, which we call a C-pair, consists of a sequence of n+1 congruences on the additive monoid N of natural numbers and a certain (n+1)×N matrix. We also give a description of the inclusion ordering of congruences in terms of a lexicographic-like ordering on C-pairs. This is then used to classify congruences on the finite d-twisted partition monoids PΦn,d, which are obtained by factoring out from PΦn the ideal of all partitions with more than d floating components. Further applications of our results, elucidating the structure and properties of the congruence lattices of the (d-)twisted partition monoids, will be the subject of a future article.
dc.format.extent65
dc.format.extent1018376
dc.language.isoeng
dc.relation.ispartofAdvances in Mathematicsen
dc.subjectPartition monoiden
dc.subjectTwisted partition monoiden
dc.subjectCongruenceen
dc.subjectCongruence latticeen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleClassification of congruences of twisted partition monoidsen
dc.typeJournal articleen
dc.contributor.sponsorEPSRCen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doi10.1016/j.aim.2021.108097
dc.description.statusPeer revieweden
dc.date.embargoedUntil2022-11-18
dc.identifier.urlhttps://arxiv.org/abs/2010.04392en
dc.identifier.grantnumberEP/S020616/1en


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