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We give upper and lower bounds for the largest integer not representable as a posi- tive linear combination of three given integers, disproving an upper bound conjectured by
In earlier work (Wilson, 2001) we derived upper and lower bounds on the mixing time of a variety of Markov chains, including Markov chains on lozenge tilings, card shuffling,
We consider the random walks killed at the boundary of the quarter plane, with homogeneous non-zero jump probabilities to the eight nearest neighbors and drift zero in the interior,
Our aim in in this section is to show that in the case of metabelian groups the lower estimate (11) can be complemented with a similar upper bound. We keep the notation of §2.. §2)
It remains to find an upper bound for the second term. Thus, we can rewrite the r.h.s. and have the same law as the number of vertices visited by the walk before the time D of its
We consider a system of nonlinear partial differential equations with stochastic dynamical boundary conditions that arises in models of neurophysiology for the diffusion of
For the plane, sphere, and hyperbolic plane we consider the canonical invariant determinan- tal point processes Z ρ with intensity ρdν, where ν is the corresponding invariant
The nine-dimensional bound is sharp: normal forms for the contact-equivalence classes of these maximally symmetric generic hyperbolic equations are derived and explicit
