Un autre q-analogue des nombres d'Euler
Séminaire lotharingien de combinatoire, Tome 42 (1998-1999)
Cet article a éte moissonné depuis 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},
year = {1998-1999},
volume = {42},
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/