Enumeration of idempotents in planar diagram monoids
MetadataShow full item record
Altmetrics Handle Statistics
Altmetrics DOI Statistics
We classify and enumerate the idempotents in several planar diagram monoids: namely, the Motzkin, Jones (a.k.a. Temperley–Lieb) and Kauffman monoids. The classification is in terms of certain vertex- and edge-coloured graphs associated to Motzkin diagrams. The enumeration is necessarily algorithmic in nature, and is based on parameters associated to cycle components of these graphs. We compare our algorithms to existing algorithms for enumerating idempotents in arbitrary (regular ⁎-) semigroups, and give several tables of calculated values.
Dolinka , I , East , J , Evangelou , A , FitzGerald , D , Ham , N , Hyde , J , Loughlin , N & Mitchell , J D 2019 , ' Enumeration of idempotents in planar diagram monoids ' , Journal of Algebra , vol. 522 , pp. 351-385 . https://doi.org/10.1016/j.jalgebra.2018.11.014
Journal of Algebra
Copyright © 2018 Elsevier Inc. All rights reserved. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.jalgebra.2018.11.014
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Showing items related by title, author, creator and subject.
Congruence lattices of finite diagram monoids East, James; Mitchell, James D.; Ruskuc, Nik; Torpey, Michael (2018-07-31) - Journal articleWe give a complete description of the congruence lattices of the following finite diagram monoids: the partition monoid, the planar partition monoid, the Brauer monoid, the Jones monoid (also known as the Temperley–Lieb ...
Computational techniques in finite semigroup theory Wilson, Wilf A. (University of St Andrews, 2019-06-25) - ThesisA semigroup is simply a set with an associative binary operation; computational semigroup theory is the branch of mathematics concerned with developing techniques for computing with semigroups, as well as investigating ...
Permutation monoids and MB-homogeneity for graphs and relational structures Coleman, Thomas D. H.; Gray, Robert; Evans, David (2019-05) - Journal articleIn 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 ...