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Séminaire Lotharingien de Combinatoire, B14b (1986).

[Formerly: Publ. I.R.M.A. Strasbourg, 1986, 323/S-14, p.
133-152.]

# Don Rawlings

# The ABC's of Classical Enumeration

**Abstract.**
Using the "arbre binaire croissant" permutation decomposition, a
relatively simple recurrence relationship is derived that
provides refinements, generalizations, and several
*q*-analogs of the Eulerian polynomials, the Euler
numbers, the Catalan numbers, the Stirling polynomials of both
the first and second kinds, the Hermite polynomials, the Bell
polynomials, and others. In several cases, the generating
functions for the *q*-analogs may be expressed in the
form of infinite products.

The paper has been finally published under the same title in
*Ann. Sci. Math. Québec* **10** (1986), 207-235.