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Recent Submissions

  • Undecidability and the developability of permutoids and rigid pseudogroups 

    Bridson, MR; Wilton, HJR (Cambridge University Press, 2017-03-20)
    A $\textit{permutoid}$ is a set of partial permutations that contains the identity and is such that partial compositions, when defined, have at most one extension in the set. In 2004 Peter Cameron conjectured that there ...
  • Four-Dimensional Weakly Self-avoiding Walk with Contact Self-attraction 

    Bauerschmidt, R; Slade, G; Wallace, BC (Springer, 2017-04-01)
    We consider the critical behaviour of the continuous-time weakly self-avoiding walk with contact self-attraction on $\mathbb{Z}$$^{4}$, for sufficiently small attraction. We prove that the susceptibility and correlation ...
  • Elliptic curves over Q$_{∞}$ are modular 

    Thorne, JA
    We show that if $\textit{p}$ is a prime, then all elliptic curves de ned over the cyclotomic $\mathbb{Z}$$_{p}$-extension of Q are modular.
  • Connective constants and height functions for Cayley graphs 

    Grimmett, Geoffrey R; Li, Zhongyang
    The connective constant $\mu$($\textit{G}$) of an infinite transitive graph $\textit{G}$ is the exponential growth rate of the number of self-avoiding walks from a given origin. In earlier work of Grimmett and Li, a locality ...

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