We consider the elementary divisors and determinant of a uniformly distributed n n random matrix with entries in the ring of integers of an arbitrary local eld. We show that the sequence of elementary divisors is in a simple bijective correspondence with a Markov chain on the nonnegative integers. The transition dynamics of this chain do not depend on the size of the matrix. As n ! 1, all but n...

In this letter, the h–analogue of Newton’s binomial formula is obtained in the h–deformed quantum plane which does not have any q–analogue. For h = 0, this is just the usual one as it should be. Furthermore, the binomial coefficients reduce to n! (n−k)! for h = 1. Some properties of the h–binomial coefficients are also given. Finally, I hope that such results will contribute to an introduction ...

Our paper provides a complete characterization of leverage and default in binomial economies with financial assets serving as collateral. Our Binomial No-Default Theorem states that any equilibrium is equivalent (in real allocations and prices) to another equilibrium in which there is no default. Thus actual default is irrelevant, though the potential for default drives the equilibrium and limi...

Our paper provides a complete characterization of leverage and default in binomial economies with financial assets serving as collateral. Our Binomial No-Default Theorem states that any equilibrium is equivalent (in real allocations and prices) to another equilibrium in which there is no default. Thus actual default is irrelevant, though the potential for default drives the equilibrium and limi...

The ^-binomial coefficient is a polynomial in q . Given an integer t and a residue class r modulo ;, a sieved ^-binomial coefficient is the sum of those terms whose exponents are congruent to r modulo /. In this paper explicit polynomial identities in q are given for sieved ij-binomial coefficients. As a limiting case, generating functions for the sieved partition function are found as multidim...

From Kemp [1], we have a family of confluent q-ChuVandermonde distributions, consisted by three members I, II and III, interpreted as a family of q-steady-state distributions from Markov chains. In this article, we provide the moments of the distributions of this family and we establish a continuous limiting behavior for the members I and II, in the sense of pointwise convergence, by applying a...

The notion of the negative q-binomial was recently introduced by Fu, Reiner, Stanton and Thiem. Mirroring the negative q-binomial, we show the classical q-Stirling numbers of the second kind can be expressed as a pair of statistics on a subset of restricted growth words. The resulting expressions are polynomials in q and 1 + q. We extend this enumerative result via a decomposition of the Stirli...