Now showing items 1-10 of 16
On convex permutations
(2011-05) - Journal article
A selection of points drawn from a convex polygon, no two with the same vertical or horizontal coordinate, yields a permutation in a canonical fashion. We characterise and enumerate those permutations which arise in this ...
Presentations of inverse semigroups, their kernels and extensions
(2011-06-01) - Journal article
Let S be an inverse semigroup and let π:S→T be a surjective homomorphism with kernel K. We show how to obtain a presentation for K from a presentation for S, and vice versa. We then investigate the relationship between the ...
On disjoint unions of finitely many copies of the free monogenic semigroup
(2013-08) - Journal article
Every semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) is finitely presented and residually finite.
Green index in semigroups : generators, presentations and automatic structures
(2012) - Journal article
The Green index of a subsemigroup T of a semigroup S is given by counting strong orbits in the complement S n T under the natural actions of T on S via right and left multiplication. This partitions the complement S nT ...
Simple extensions of combinatorial structures
(2011-07) - Journal article
An interval in a combinatorial structure R is a set I of points which are related to every point in R \ I in the same way. A structure is simple if it has no proper intervals. Every combinatorial structure can be expressed ...
Substitution-closed pattern classes
(2011-02) - Journal article
The substitution closure of a pattern class is the class of all permutations obtained by repeated substitution. The principal pattern classes (those defined by a single restriction) whose substitution closure can be defined ...
Generators and relations for subsemigroups via boundaries in Cayley graphs
(2011-11) - Journal article
Given a finitely generated semigroup S and subsemigroup T of S we define the notion of the boundary of T in S which, intuitively, describes the position of T inside the left and right Cayley graphs of S. We prove that if ...
Free monoids are coherent
(2017-02) - Journal article
A monoid S is said to be right coherent if every finitely generated subact of every finitely presented right S-act is finitely presented. Left coherency is defined dually and S is coherent if it is both right and left ...
Unary FA-presentable semigroups
(2012-06-08) - Journal article
Automatic presentations, also called FA-presentations, were introduced to extend nite model theory to innite structures whilst retaining the solubility of interesting decision problems. A particular focus of research has ...
Subalgebras of FA-presentable algebras
(2014-06) - Journal article
Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. This paper studies FA-presentable ...