Geodesic
The Descent Statistic on 123-avoiding Permutations
Séminaire lotharingien de combinatoire, Tome 63 (2010) 
Marilena Barnabei; Flavio Bonetti; Matteo Silimbani. The Descent Statistic on 123-avoiding Permutations. Séminaire lotharingien de combinatoire, Tome 63 (2010). http://geodesic.mathdoc.fr/item/SLC_2010_63_a0/
@article{SLC_2010_63_a0,
     author = {Marilena Barnabei and Flavio Bonetti and Matteo Silimbani},
     title = {The {Descent} {Statistic} on 123-avoiding {Permutations}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2010},
     volume = {63},
     url = {http://geodesic.mathdoc.fr/item/SLC_2010_63_a0/}
}
TY  - JOUR
AU  - Marilena Barnabei
AU  - Flavio Bonetti
AU  - Matteo Silimbani
TI  - The Descent Statistic on 123-avoiding Permutations
JO  - Séminaire lotharingien de combinatoire
PY  - 2010
VL  - 63
UR  - http://geodesic.mathdoc.fr/item/SLC_2010_63_a0/
ID  - SLC_2010_63_a0
ER  - 
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%A Flavio Bonetti
%A Matteo Silimbani
%T The Descent Statistic on 123-avoiding Permutations
%J Séminaire lotharingien de combinatoire
%D 2010
%V 63
%U http://geodesic.mathdoc.fr/item/SLC_2010_63_a0/
%F SLC_2010_63_a0

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

We exploit Krattenthaler's bijection between 123-avoiding permutations and Dyck paths to determine the Eulerian distribution over the set Sn(123) of 123-avoiding permutations in Sn. In particular, we show that the descents of a permutation correspond to valleys and triple ascents of the associated Dyck path. We get the Eulerian numbers of Sn(123) by studying the joint distribution of these two statistics on Dyck paths.