Journal of Integer Sequences, Vol. 16 (2013), Article 13.3.8

Two Permutation Classes Enumerated by the Central Binomial Coefficients

Marilena Barnabei and Flavio Bonetti
Dipartimento di Matematica
Università di Bologna
Piazza di Porta San Donato 5
40126 Bologna

Matteo Silimbani
LaBRI — Université Bordeaux 1
351, cours de la Libération
33405 Talence


We define a map between the set of permutations that avoid either the four patterns 3214, 3241, 4213, 4231 or 3124, 3142, 4123, 4132, and the set of Dyck prefixes. This map, when restricted to either of the two classes, turns out to be a bijection that allows us to determine some notable features of these permutations, such as the distribution of the statistics "number of ascents", "number of left-to-right maxima", "first element", and "position of the maximum element".

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(Concerned with sequence A000984 A001263 A039599.)

Received January 9 2013; revised version received February 24 2013. Published in Journal of Integer Sequences, March 2 2013.

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