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.
M. Barnabei, F. Bonetti, M. Silimbani (2010). The Descent Statistic on 123-avoiding Permutations. SÉMINAIRE LOTHARINGIEN DE COMBINATOIRE, 63, 1-7.
The Descent Statistic on 123-avoiding Permutations
BARNABEI, MARILENA;BONETTI, FLAVIO;SILIMBANI, MATTEO
2010
Abstract
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.File in questo prodotto:
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