31 citations · 211 across the 34 of their papers we have counts for
6 papers · 1 filter
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…
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…
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…
Structural aspects of semigroups based on digraphs
James East, Maximilien Gadouleau, James D. Mitchell
Given any digraph without loops or multiple arcs, there is a natural construction of a semigroup of transformations. To every arc of is associate…
Enumeration of idempotents in planar diagram monoids
Igor Dolinka, James East, Athanasios Evangelou +5
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…