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Two Permutation Classes Enumerated by the Central Binomial Coefficients
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Marilena Barnabei and Flavio Bonetti

Dipartimento di Matematica

Università di Bologna

Piazza di Porta San Donato 5

40126 Bologna

Italy

Matteo Silimbani

LaBRI — Université Bordeaux 1

351, cours de la Libération

33405 Talence

France

**Abstract:**

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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