The/?-adic order, vp(r), of r is the exponent of the highest power of a prime/? which divides r. We characterize the/?-adic order vp(Fn) of the F„ sequence using multisection identities. The method of multisection is a helpful tool in discovering and proving divisibility properties. Here it leads to invariants of the modulo p Fibonacci generating function for p ^ 5. The proof relies on some sim...

We prove divisibility properties for sums of powers of binomial coefficients and of q-binomial coefficients. Dedicated to the memory of Paul Erdős

Results about the laws of the perpetuity and remainder variables associated to a subordinator are presented, with particular emphasis on their Mellin transforms, and multiplicative infinite divisibility property. Previous results by Bertoin-Yor (2001) are incorporated in our discussion; important examples when the subordinator is the inverse local time of a diffusion are exhibited. Results of U...

We consider a variant of the standard Arrow{Debreu model which contains a number of indivisible goods and one perfectly divisible good (numeraire or money). The objective of this paper is to clarify a general mathematical mechanism which guarantees the existence of an equilibrium in such a model. It is shown that the crucial condition for the existence of an equilibrium is that the sets of supp...

Consider a model of location choice by two sorts of agents, called “buyers”and “sellers:”In the first period agents simultaneously choose between two identical possible locations; following this, the agents at each location play some sort of game with the other agents there. Buyers prefer locations with fewer other buyers and more sellers, and sellers have the reverse preferences. We study the ...

Ramachandran (1969) [9, Theorem 8] has shown that for any univariate infinitely divisible distribution and any positive real number α, an absolute moment of order α relative to the distribution exists (as a finite number) if and only if this is so for a certain truncated version of the corresponding Lévy measure. A generalized version of this result in the case of multivariate infinitely divisi...

We use the class equation of a finite group action together with Burnside’s orbit counting theorem to derive classical divisibility theorems.