Séminaire Lotharingien de Combinatoire, B42e (1999), 22 pp.

G.-N. Han, A. Randrianarivony, J. Zeng

Un autre q-analogue des nombres d'Euler

Abstract. The ordinary generating functions of the secant and tangent numbers have very simple continued fraction expansions. However, the classical q-secant and q-tangent numbers do not give a natural q-analogue of these continued fractions. In this paper, we introduce a different q-analogue of Euler numbers using q-difference operator and show that their generating functions have simple continued fraction expansions. Furthermore, by establishing an explicit bijection between some Motzkin paths and (k,r)-multipermutations we derive combinatorial interpretations for these q-numbers. Finally the allied q-Euler median numbers are also studied.

Received: December 16, 1998; Accepted: February 24, 1999.

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