Séminaire Lotharingien de Combinatoire, B30h (1993).
[Formerly: Publ. I.R.M.A. Strasbourg, 1993, 1993/034, p.
Probabilistic Interpretations of q-Analogues
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),
Bernoulli trials and number theory, Amer. Math. Monthly 101 (1994),