31 citations · 211 across the 34 of their papers we have counts for
51 papers
Faithful linear and relational representations of diagram categories and monoids
James East, Marianne Johnson, Mark Kambites
We study representations of diagram categories by binary relations and matrices over rings and semirings. Our main result is a faithful involutive tensor representation of the part…
A groupoid approach to regular -semigroups
James East, P. A. Azeef Muhammed
In this paper we develop a new groupoid-based structure theory for the class of regular -semigroups. This class occupies something of a `sweet spot' between the important classe…
Product decompositions of semigroups induced by action pairs
Scott Carson, Igor Dolinka, James East +2
This paper concerns a class of semigroups that arise as products , associated to what we call `action pairs'. Here and are subsemigroups of a common monoid and, roughly…
Presentations for wreath products involving symmetric inverse monoids and categories
Chad Clark, James East
Wreath products involving symmetric inverse monoids/semigroups/categories arise in many areas of algebra and science, and presentations by generators and relations are crucial tool…
On the enumeration of integer tetrahedra
James East, Michael Hendriksen, Laurence Park
We consider the problem of enumerating integer tetrahedra of fixed perimeter (sum of side-lengths) and/or diameter (maximum side-length), up to congruence. As we will see, this pro…
Minimum degrees of finite rectangular bands, null semigroups, and variants of full transformation semigroups
Peter J Cameron, James East, Des FitzGerald +3
For a positive integer , the full transformation semigroup consists of all self maps of the set under composition. Any finite semigroup embeds in some…
Presentations for P^K
James East
It is a classical result that the direct product AxB of two groups is finitely generated (finitely presented) if and only if A and B are both finitely generated (finitely presented…
Generating wreath products of symmetric and alternating groups
James East, James D Mitchell
We show that the wreath product of two finite symmetric or alternating groups is 2-generated.
Presentations for Temperley-Lieb algebras
James East
We give a new and conceptually straightforward proof of the well-known presentation for the Temperley-Lieb algebra, via an alternative new presentation. Our method involves twisted…
Ehresmann theory and partition monoids
James East, Robert D. Gray
This article concerns Ehresmann structures in the partition monoid . Since contains the symmetric and dual symmetric inverse monoids on the same base set , it natural…
Properties of congruences of twisted partition monoids and their lattices
James East, Nik Ruskuc
We build on the recent characterisation of congruences on the infinite twisted partition monoids and their finite -twisted homomorphic images $\mathcal{P}_{n…
Classification of congruences of twisted partition monoids
James East, Nik Ruskuc
The twisted partition monoid is an infinite monoid obtained from the classical finite partition monoid by taking into account the number of floati…
Generating the monoid of matrices over max-plus and min-plus semirings
James East, Julius Jonušas, J. D. Mitchell
In this short note, we describe generating sets for the monoids of consisting of all matrices over certain finite tropical semirings.
Presentations for tensor categories
James East
We introduce new techniques for working with presentations for a large class of (strict) tensor categories. We then apply the general theory to obtain presentations for partition,…
Congruence lattices of ideals in categories and (partial) semigroups
James East, Nik Ruskuc
This paper presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their id…
Structure of principal one-sided ideals
James East
We give a thorough structural analysis of the principal one-sided ideals of arbitrary semigroups, and then apply this to full transformation semigroups and symmetric inverse monoid…
Sandwich semigroups in diagram categories
Ivana Đurđev, Igor Dolinka, James East
This paper concerns a number of diagram categories, namely the partition, planar partition, Brauer, partial Brauer, Motzkin and Temperley-Lieb categories. If denotes a…
Idempotents and one-sided units: Lattice invariants and a semigroup of functors on the category of monoids
James East
For a monoid , we denote by the group of units, the submonoid generated by the idempotents, and and the submonoid…
Green's relations and stability for subsemigroups
James East, Peter M. Higgins
We prove new results on inheritance of Green's relations by subsemigroups in the presence of stability of elements. We provide counterexamples in other cases to show in particular…
Lattice paths and submonoids of
James East, Nicholas Ham
We study a number of combinatorial and algebraic structures arising from walks on the two-dimensional integer lattice. To a given step set , there are two na…
Congruences on infinite partition and partial Brauer monoids
James East, Nik Ruskuc
We give a complete description of the congruences on the partition monoid and the partial Brauer monoid , where is an arbitrary infinite set, and also of the lattic…
Transformation representations of sandwich semigroups
James East
Let be an element of a semigroup . The local subsemigroup of with respect to is the subsemigroup of . The variant of with respect to is the semigrou…
Integer polygons of given perimeter
James East, Ron Niles
A classical result of Honsberger states that the number of incongruent triangles with integer sides and perimeter is the nearest integer to ( even) or $\fra…
Sandwich semigroups in locally small categories II: Transformations
Igor Dolinka, Ivana Ðurđev, James East +4
Fix sets and , and write for the set of all partial functions . Fix a partial function , and define the operation on $\mathca…