Séminaire Lotharingien de Combinatoire, B63a (2010), 7 pp.

Marilena Barnabei, Flavio Bonetti and Matteo Silimbani

The Descent Statistic on 123-avoiding Permutations

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.

Received: October 6, 2009. Accepted: January 4, 2010. Final Version: January 12, 2010.

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