The distribution of consecutive patterns of length 3 in 3\textrm-1\textrm-2-avoiding permutations

2009/04/01 by Barnabei, M., Bonetti, F., Silimbani, M.
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.0904.0079

Abstract

We exploit Krattenthaler's bijection between the set S_n(3\textrm-1\textrm-2) of permutations in S_n avoiding the classical pattern 3\textrm-1\textrm-2 and Dyck n-paths to study the distribution of every consecutive pattern of length 3 on the set S_n(3\textrm-1\textrm-2). We show that these consecutive patterns split into 3 equidistribution classes, by means of an involution on Dyck paths due to E.Deutsch. In addition, we state equidistribution theorems concerning triplets of statistics relative to the occurrences of the consecutive patterns of length 3 in a permutation.

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