Pure Mathematics

 

Main areas of research activity are algebra, including group theory, semigroup theory, lattice theory, and computational group theory, and analysis, including fractal geometry, multifractal analysis, complex dynamical systems, Kleinian groups, and diophantine approximations.

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Recent Submissions

  • Orderings on words and permutations 

    McDevitt, Matthew (University of St Andrews, 2019-12-03) - Thesis
    Substructure orderings are ubiquitous throughout combinatorics and all of mathematics. In this thesis we consider various orderings on words, as well as the consecutive involvement ordering on permutations. Throughout ...

  • Assouad type dimensions and dimension spectra 

    Yu, Han (University of St Andrews, 2019-12-03) - Thesis
    In the first part of this thesis we introduce a new dimension spectrum motivated by the Assouad dimension; a familiar notion of dimension which, for a given metric space, returns the minimal exponent α ≥ 0 such that for ...

  • Semigroup congruences : computational techniques and theoretical applications 

    Torpey, Michael (University of St Andrews, 2019-06-25) - Thesis
    Computational semigroup theory is an area of research that is subject to growing interest. The development of semigroup algorithms allows for new theoretical results to be discovered, which in turn informs the creation ...

  • Maximal subsemigroups of finite transformation and diagram monoids 

    East, James; Kumar, Jitender; Mitchell, James D.; Wilson, Wilf A. (2018-06-15) - Journal article
    We describe and count the maximal subsemigroups of many well-known transformation monoids, and diagram monoids, using a new unified framework that allows the treatment of several classes of monoids simultaneously. The ...

  • Computing maximal subsemigroups of a finite semigroup 

    Donoven, C. R.; Mitchell, J. D.; Wilson, W. A. (2018-07-01) - Journal article
    A proper subsemigroup of a semigroup is maximal if it is not contained in any other proper subsemigroup. A maximal subsemigroup of a finite semigroup has one of a small number of forms, as described in a paper of Graham, ...

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