Résumé
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.
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Han, GN., Randrianarivony, A., Zeng, J. (2001). Un autre q-analogue des nombres d’Euler. In: Foata, D., Han, GN. (eds) The Andrews Festschrift. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56513-7_5
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DOI: https://doi.org/10.1007/978-3-642-56513-7_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41491-9
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