Now showing items 1-20 of 33

  • Automatic presentations and semigroup constructions 

    Cain, Alan J.; Oliver, Graham; Ruskuc, Nik; Thomas, Richard M. (2010-08) - Journal article
    An 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 

    Cain, Alan James; Oliver, Graham; Ruskuc, Nik; Thomas, Richard M. (2009-11) - Journal article
    This paper applies the concept of FA-presentable structures to semigroups. We give a complete classification of the finitely generated FA-presentable cancellative semigroups: namely, a finitely generated cancellative ...
  • Cancellative and Malcev presentations for finite Rees index subsemigroups and extensions 

    Cain, Alan James; Robertson, Edmund Frederick; Ruskuc, Nik (2008-02) - Journal article
    It 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 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 ...
  • Every group is a maximal subgroup of the free idempotent generated semigroup over a band 

    Dolinka, I; Ruskuc, Nik (2013-05) - Journal article
    Given 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 

    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 ...
  • Finite groups are big as semigroups 

    Dolinka, Igor; Ruskuc, Nik (2011-09) - Journal article
    We 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 

    Gould, V; Hartmann, M; Ruskuc, Nik (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 ...
  • Generators and relations for subsemigroups via boundaries in Cayley graphs 

    Gray, R; Ruskuc, Nik (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 ...
  • Geometric grid classes of permutations 

    Albert, M.H.; Atkinson, M.D.; Bouvel, M.; Ruskuc, Nik; Vatter, V. (2013-11) - Journal article
    A 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 

    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 ...
  • Green index and finiteness conditions for semigroups 

    Gray, Robert Duncan; Ruskuc, Nik (2008-10-15) - Journal article
    Let 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 

    Cain, A.J.; Gray, R; Ruskuc, Nik (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 ...
  • Growth of generating sets for direct powers of classical algebraic structures 

    Quick, Martyn; Ruskuc, Nik (2010-08) - Journal article
    For 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) 

    Albert, M.H.; Atkinson, M.D.; Brignall, R; Ruskuc, Nik; Smith, R; West, J (2010-10-22) - Journal article
    Pattern 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 

    Huczynska, Sophie; Ruskuc, Nik (2015-07) - Journal article
    Combinatorial 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 

    Albert, M.D.; Ruskuc, Nik; Vatter, V. (2015-02) - Journal article
    Geometric 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 idempotent-generated semigroups over the full transformation monoid 

    Gray, R; Ruskuc, Nik (2012-05) - Journal article
    Let 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 

    Albert, M.H.; Linton, Stephen Alexander; Ruskuc, Nik; Vatter, V; Waton, S (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 ...
  • On disjoint unions of finitely many copies of the free monogenic semigroup 

    Abughazalah, Nabilah; Ruskuc, Nik (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.