Now showing items 1-20 of 21

    • Adventures in applying iteration lemmas 

      Pfeiffer, Markus Johannes (University of St Andrews, 2013-06-28) - Thesis
      The 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 S-acts and inverse semigroup presentations 

      Dombi, Erzsebet Rita (University of St Andrews, 2005) - Thesis
      To 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 

      Descalco, L. (University of St Andrews, 2002) - Thesis
      In 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 

      McLeman, Alexander Lewis Andrew (University of St Andrews, 2015-06-26) - Thesis
      Let 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 

      Distler, Andreas (University of St Andrews, 2010-06-23) - Thesis
      The 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 2-generated subgroups of the group of homeomorphisms of Cantor space 

      Hyde, James Thomas (University of St Andrews, 2017) - Thesis
      We study finite generation, 2-generation 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 star-height problem for regular languages 

      Bourne, Thomas (University of St Andrews, 2017-12-07) - Thesis
      The Generalised Star-Height 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 

      Awang, Jennifer S. (University of St Andrews, 2015-06-26) - Thesis
      Geometric 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 

      Craik, Simon (University of St Andrews, 2013) - Thesis
      The 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 

      Mitchell, James David (University of St Andrews, 2002-07) - Thesis
      In 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 

      Abu-Ghazalh, Nabilah Hani (University of St Andrews, 2013-06-28) - Thesis
      In 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 

      Thomson, Michael R. (University of St Andrews, 2001) - Thesis
      The 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 

      Carey, Rachael Marie (University of St Andrews, 2016-06-24) - Thesis
      In this thesis we examine properties and constructions of graph automatic semigroups, a generalisation of both automatic semigroups and finitely generated FA-presentable semigroups. We consider the properties of graph ...
    • Intersection problems in combinatorics 

      Brunk, Fiona (University of St Andrews, 2009-11-30) - Thesis
      With the publication of the famous Erdős-Ko-Rado Theorem in 1961, intersection problems became a popular area of combinatorics. A family of combinatorial objects is t-intersecting if any two of its elements mutually ...
    • On generators, relations and D-simplicity of direct products, Byleen extensions, and other semigroup constructions 

      Baynes, Samuel (University of St Andrews, 2015-11-30) - Thesis
      In 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 

      Waton, Stephen D. (University of St Andrews, 2007-06-19) - Thesis
      The 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 star-height of subword counting languages and their relationship to Rees zero-matrix semigroups 

      Bourne, Tom; Ruškuc, Nik (2016-11-15) - Journal article
      Given a word w over a finite alphabet, we consider, in three special cases, the generalised star-height of the languages in which w occurs as a contiguous subword (factor) an exact number of times and of the languages in ...
    • Semigroup presentations 

      Ruškuc, Nik (University of St Andrews, 1995) - Thesis
      In 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 

      Brignall, Robert (University of St Andrews, 2007-11-30) - Thesis
      The 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 

      Schaefer, Artur (University of St Andrews, 2016) - Thesis
      The 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. ...