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.