A probabilistic approach to q-polynomial coefficients, Euler and Stirling numbers

2004/07/02 by А. И. Ильинский, Alexander I. Il'inskii, Il'inskii, Alexander I.
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Mathematical functions and polynomials #math.CO #math.PR #msc:05A30 #msc:11B65

paper · pdf · doi:10.48550/arxiv.math/0407029

27 pages

arxiv created 2004/07/02 · arxiv updated 2009/12/01

Abstract

It is known that Bernoulli scheme of independent trials with two outcomes is connected with the binomial coefficients. The aim of this paper is to indicate stochastic processes which are connected with the q-polynomial coefficients (in particular, with the q-binomial coefficients, or the Gaussian polynomials), Stirling numbers of the first and the second kind, and Euler numbers in a natural way. A probabilistic approach allows us to give very simple proofs of some identities for these coefficients.

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