Séminaire Lotharingien de Combinatoire, B63a (2010), 7 pp.
Marilena Barnabei, Flavio Bonetti and Matteo Silimbani
The Descent Statistic on 123-avoiding Permutations
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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