Browsing by Name "Ruškuc, Nik"
Now showing items 120 of 21

Adventures in applying iteration lemmas
(University of St Andrews, 20130628)  ThesisThe word problem of a finitely generated group is commonly defined to be a formal language over a finite generating set. The class of finite groups has been characterised as the class of finitely generated groups that ... 
Automatic Sacts and inverse semigroup presentations
(University of St Andrews, 2005)  ThesisTo provide a general framework for the theory of automatic groups and semigroups, we introduce the notion of an automatic semigroup act. This notion gives rise to a variety of definitions for automaticity depending on the ... 
Automatic semigroups : constructions and subsemigroups
(University of St Andrews, 2002)  ThesisIn this thesis we start by considering conditions under which some standard semigroup constructions preserve automaticity. We first consider Rees matrix semigroups over a semigroup, which we call the base, and work on the ... 
Cayley automaton semigroups
(University of St Andrews, 20150626)  ThesisLet S be a semigroup, C(S) the automaton constructed from the right Cayley graph of S with respect to all of S as the generating set and ∑(C(S)) the automaton semigroup constructed from C(S). Such semigroups are ... 
Classification and enumeration of finite semigroups
(University of St Andrews, 20100623)  ThesisThe classification of finite semigroups is difficult even for small orders because of their large number. Most finite semigroups are nilpotent of nilpotency rank 3. Formulae for their number up to isomorphism, and up ... 
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 ... 
Counting subwords and other results related to the generalised starheight problem for regular languages
(University of St Andrews, 20171207)  ThesisThe Generalised StarHeight Problem is an open question in the field of formal language theory that concerns a measure of complexity on the class of regular languages; specifically, it asks whether or not there exists an ... 
Dots and lines : geometric semigroup theory and finite presentability
(University of St Andrews, 20150626)  ThesisGeometric semigroup theory means different things to different people, but it is agreed that it involves associating a geometric structure to a semigroup and deducing properties of the semigroup based on that structure. ... 
Ends of semigroups
(University of St Andrews, 2013)  ThesisThe aim of this thesis is to understand the algebraic structure of a semigroup by studying the geometric properties of its Cayley graph. We define the notion of the partial order of ends of the Cayley graph of a semigroup. ... 
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 ... 
Finiteness conditions for unions of semigroups
(University of St Andrews, 20130628)  ThesisIn this thesis we prove the following: The semigroup which is a disjoint union of two or three copies of a group is a Clifford semigroup, Rees matrix semigroup or a combination between a Rees matrix semigroup and a ... 
Finiteness conditions of wreath products of semigroups and related properties of diagonal acts
(University of St Andrews, 2001)  ThesisThe purpose of this thesis is to consider finite generation, finite presentability and related properties of restricted wreath products of semigroups. We show that the wreath product Awr B of two monoids is finitely generated ... 
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 ... 
Intersection problems in combinatorics
(University of St Andrews, 20091130)  ThesisWith the publication of the famous ErdősKoRado Theorem in 1961, intersection problems became a popular area of combinatorics. A family of combinatorial objects is tintersecting if any two of its elements mutually ... 
On generators, relations and Dsimplicity of direct products, Byleen extensions, and other semigroup constructions
(University of St Andrews, 20151130)  ThesisIn this thesis we study two different topics, both in the context of semigroup constructions. The first is the investigation of an embedding problem, specifically the problem of whether it is possible to embed any given ... 
On permutation classes defined by token passing networks, gridding matrices and pictures : three flavours of involvement
(University of St Andrews, 20070619)  ThesisThe study of pattern classes is the study of the involvement order on finite permutations. This order can be traced back to the work of Knuth. In recent years the area has attracted the attention of many combinatoralists ... 
On the starheight of subword counting languages and their relationship to Rees zeromatrix semigroups
(20161115)  Journal articleGiven a word w over a finite alphabet, we consider, in three special cases, the generalised starheight of the languages in which w occurs as a contiguous subword (factor) an exact number of times and of the languages in ... 
Semigroup presentations
(University of St Andrews, 1995)  ThesisIn this thesis we consider in detail the following two fundamental problems for semigroup presentations: 1. Given a semigroup find a presentation defining it. 2. Given a presentation describe the semigroup defined by ... 
Simplicity in relational structures and its application to permutation classes
(University of St Andrews, 20071130)  ThesisThe simple relational structures form the units, or atoms, upon which all other relational structures are constructed by means of the substitution decomposition. This decomposition appears to have first been introduced in ... 
Synchronizing permutation groups and graph endomorphisms
(University of St Andrews, 2016)  ThesisThe current thesis is focused on synchronizing permutation groups and on graph endo morphisms. Applying the implicit classification of rank 3 groups, we provide a bound on synchronizing ranks of rank 3 groups, at first. ...