Browsing by Name "Ruskuc, Nik"
Now showing items 120 of 33

Automatic presentations and semigroup constructions
(201008)  Journal articleAn automatic presentation for a relational structure is, informally, an abstract representation of the elements of that structure by means of a regular language such that the relations can all be recognized by finite ... 
Automatic presentations for semigroups
(200911)  Journal articleThis paper applies the concept of FApresentable structures to semigroups. We give a complete classification of the finitely generated FApresentable cancellative semigroups: namely, a finitely generated cancellative ... 
Cancellative and Malcev presentations for finite Rees index subsemigroups and extensions
(200802)  Journal articleIt is known that, for semigroups, the property of admitting a finite presentation is preserved on passing to subsemigroups and extensions of finite Rees index. The present paper shows that the same holds true for Malcev, ... 
Constructing 2generated subgroups of the group of homeomorphisms of Cantor space
(University of St Andrews, 2017)  ThesisWe study finite generation, 2generation and simplicity of subgroups of H[sub]c, the group of homeomorphisms of Cantor space. In Chapter 1 and Chapter 2 we run through foundational concepts and notation. In Chapter 3 we ... 
Every group is a maximal subgroup of the free idempotent generated semigroup over a band
(201305)  Journal articleGiven an arbitrary group G we construct a semigroup of idempotents (band) BG with the property that the free idempotent generated semigroup over BG has a maximal subgroup isomorphic to G. If G is finitely presented then ... 
Extremal problems in combinatorial semigroup theory
(University of St Andrews, 200207)  ThesisIn this thesis we shall consider three types of extremal problems (i.e. problems involving maxima and minima) concerning semigroups. In the first chapter we show how to construct a minimal semigroup presentation that defines ... 
Finite groups are big as semigroups
(201109)  Journal articleWe prove that a finite group G occurs as a maximal proper subsemigroup of an infinite semigroup (in the terminology of Freese, Ježek, and Nation, G is a big semigroup) if and only if G ≥ 3. In fact, any finite semigroup ... 
Free monoids are coherent
(201702)  Journal articleA monoid S is said to be right coherent if every finitely generated subact of every finitely presented right Sact is finitely presented. Left coherency is defined dually and S is coherent if it is both right and left ... 
Generators and relations for subsemigroups via boundaries in Cayley graphs
(201111)  Journal articleGiven 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 ... 
Geometric grid classes of permutations
(201311)  Journal articleA geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope ±1 arranged in a rectangular pattern governed by a matrix. Using a mixture of geometric and language ... 
Graph automatic semigroups
(University of St Andrews, 20160624)  ThesisIn this thesis we examine properties and constructions of graph automatic semigroups, a generalisation of both automatic semigroups and finitely generated FApresentable semigroups. We consider the properties of graph ... 
Green index and finiteness conditions for semigroups
(20081015)  Journal articleLet S be a semigroup and let T be a subsemigroup of S. Then T acts on S by left and by right multiplication. If the complement S \ T has finitely many strong orbits by both these actions we say that T has finite Green index ... 
Green index in semigroups : generators, presentations and automatic structures
(2012)  Journal articleThe 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 ... 
Growth of generating sets for direct powers of classical algebraic structures
(201008)  Journal articleFor an algebraic structure A denote by d(A) the smallest size of a generating set for A, and let d(A)=(d(A),d(A2),d(A3),…), where An denotes a direct power of A. In this paper we investigate the asymptotic behaviour of the ... 
Growth rates for subclasses of Av(321)
(20101022)  Journal articlePattern classes which avoid 321 and other patterns are shown to have the same growth rates as similar (but strictly larger) classes obtained by adding articulation points to any or all of the other patterns. The method of ... 
Homomorphic image orders on combinatorial structures
(201507)  Journal articleCombinatorial structures have been considered under various orders, including substructure order and homomorphism order. In this paper, we investigate the homomorphic image order, corresponding to the existence of a ... 
Inflations of geometric grid classes of permutations
(201502)  Journal articleGeometric grid classes and the substitution decomposition have both been shown to be fundamental in the understanding of the structure of permutation classes. In particular, these are the two main tools in the recent ... 
Maximal subgroups of free idempotentgenerated semigroups over the full transformation monoid
(201205)  Journal articleLet Tn be the full transformation semigroup of all mappings from the set {1, . . . , n} to itself under composition. Let E = E(Tn) denote the set of idempotents of Tn and let e ∈ E be an arbitrary idempotent satisfying im ... 
On convex permutations
(201105)  Journal articleA 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 ... 
On disjoint unions of finitely many copies of the free monogenic semigroup
(201308)  Journal articleEvery semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) is finitely presented and residually finite.