For q = p, the graph G∗(q) is called the qth Platonic graph. The name comes from the fact that when p = 3 or 5, the graphs G∗(p) correspond to 1-skeletons of two of the Platonic solids, in other words, the tetrahedron and the icosahedron as in [2]. More generally, G∗(p) is the 1-skeleton […]

This paper continues the authors previous work that deals with the problem of reconstructing some function defined on a finite group G from averages of the function over various neighborhoods of points. It generalizes work done earlier by Diaconis and Graham, and Fill, among others. Diaconis and Graham discuss the cases where G = Zk2, […]

In this paper, we study the dual transformation applied to N particles and N −1 springs that are no longer constrained to the real line. For simplicity, assume the Hamiltonian system formed to be embedded in Euclidean n−space with the standard metric and also assume that N < ∞ and that all N particles are […]

Although Kloosterman sums of odd prime powers have been studied extensively, many authors avoid the case where p = 2. This case is important as Kloosterman sums for fields of characteristic 2 have been useful in error-correcting codes and Kloosterman sums over the ring of integers modulo pr have been helpful in studying the spectra […]