In this paper we investigate the Erd¨os/Falconer distance conjecture for a natural class of sets statistically, though not necessarily arithmetically, similar to a lattice. We pr...
Numerical simulations in computational physics, biology, and finance, often require the use of high quality and efficient parallel random number generators. We design and optimi...
David A. Bader, Aparna Chandramowlishwaran, Virat ...
In order to investigate the routing aspects of small-world networks, Kleinberg [13] proposes a network model based on a d-dimensional lattice with long-range links chosen at random...
Catalan numbers C(n) = 1 n+1 2n n enumerate binary trees and Dyck paths. The distribution of paths with respect to their number k of factors is given by ballot numbers B(n, k) = n-...
Abstract. We consider lattice walks in the plane starting at the origin, remaining in the first quadrant i, j ≥ 0 and made of West, South and North-East steps. In 1965, Germain ...