  We formulate a dynamically triangulated model of three-dimensional Lorentzian
quantum gravity whose spatial sections are flat two-tori. It is shown that the
combinatorics involved in evaluating the one-step propagator (the transfer
matrix) is that of a set of vicious walkers on a two-dimensional lattice with
periodic boundary conditions and that the entropy of the model scales
exponentially with the volume. We also give explicit expressions for the
Teichm\"uller parameters of the spatial slices in terms of the discrete
parameters of the 3d triangulations, and reexpress the discretized action in
terms of them. The relative simplicity and explicitness of this model make it
ideally suited for an analytic study of the conformal-factor cancellation
observed previously in Lorentzian dynamical triangulations and of its relation
to alternative, reduced phase space quantizations of 3d gravity.
