Séminaire Lotharingien de Combinatoire, B30h (1993).
[Formerly: Publ. I.R.M.A. Strasbourg, 1993, 1993/034, p. 111-114.]

Don Rawlings

Probabilistic Interpretations of q-Analogues

Abstract. In some instances, the parameter q of a q-analogue may be directly identified as the probability of tails occurring in a Bernoulli trials scheme. The simple coin-tossing game presented in the next section gives rise to a q-analogue of a standard limit formula for the exponential function and to a q-analogue of Euler's product formula for the Riemann zeta function. The context in which these q-identities arise bears some resemblance to the one Gilbert Labelle used in obtaining a q-analogue of Euler's gamma function. Slight variations of the same game also lead to probabilistic interpretations of the inversion number and of the major index.

This paper is a summary of:

Bernoulli trials and permutation statistics, Internat. J. Math. Math. Sci. 15 (1992), 291--311

Bernoulli trials and number theory, Amer. Math. Monthly 101 (1994), 948--952.