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

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

2004-07-02

arxiv.org/abs/math/0407029v1

Mathematics

Combinatorics

27 pages

Scientific paper

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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