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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