Un autre q-analogue des nombres d'Euler
Séminaire lotharingien de combinatoire, Tome 42 (1998-1999)
Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website
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.
@article{SLC_1998-1999_42_a5,
author = {G.-N. Han and A. Randrianarivony and J. Zeng},
title = {Un autre q-analogue des nombres {d'Euler}},
journal = {S\'eminaire lotharingien de combinatoire},
publisher = {mathdoc},
volume = {42},
year = {1998-1999},
url = {http://geodesic.mathdoc.fr/item/SLC_1998-1999_42_a5/}
}
G.-N. Han; A. Randrianarivony; J. Zeng. Un autre q-analogue des nombres d'Euler. Séminaire lotharingien de combinatoire, Tome 42 (1998-1999). http://geodesic.mathdoc.fr/item/SLC_1998-1999_42_a5/