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

  • Highest rank of a polytope for An 

    Cameron, Peter Jephson; Fernandes, Maria Elisa; Leemans, Dimitri; Mixer, Mark (2017-04-28) - Journal article
    We prove that the highest rank of a string C-group constructed from an alternating group Altn is 0 if n = 3, 4, 6, 7, 8; 3 if n = 5; 4 if n = 9; 5 if n = 10; 6 if n = 11; and the floor of (n-1)/2 if n ≥ 12. This solves a ...
  • Planar self-affine sets with equal Hausdorff, box and affinity dimensions 

    Falconer, Kenneth; Kempton, Thomas Michael William (2016-10-20) - Journal article
    Using methods from ergodic theory along with properties of the Furstenberg measure we obtain conditions under which certain classes of plane self-affine sets have Hausdorff or box-counting dimensions equal to their affinity ...
  • Generating sets of finite groups 

    Cameron, Peter Jephson; Lucchini, Andrea; Roney-Dougal, Colva Mary (2017-04-02) - Journal article
    We investigate the extent to which the exchange relation holds in finite groups G. We define a new equivalence relation ≡m, where two elements are equivalent if each can be substituted for the other in any generating set ...
  • Mixed moments and local dimensions of measures 

    Olsen, Lars Ole Ronnow (2016-09-01) - Journal article
    We analyse the asymptotic behaviour of the mixed moments of Borel probability measures on [0,1]d. In particular, we prove that the asymptotic behaviour of the mixed moments of a measure is intimately related to the local ...
  • On the generating graph of a simple group 

    Lucchini, Andrea; Maroti, Attila; Roney-Dougal, Colva Mary (2016-09-26) - Journal article
    The generating graph Γ(H) of a finite group H is the graph defined on the elements of H, with an edge between two vertices if and only if they generate H. We show that if H is a sufficiently large simple group with Γ(G) ≅ ...

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