The descent statistic over 123-avoiding permutations

Details The descent statistic over 123-avoiding permutations The descent statistic over 123-avoiding permutations

2009-10-06

arxiv.org/abs/0910.0963v1

Mathematics

Combinatorics

8 pages, 4 figures

Scientific paper

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

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