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Séminaire Lotharingien de Combinatoire, B61Ah (2010), 29 pp.

# Nicolas Bonichon, Mireille Bousquet-Mélou and Éric Fusy

# Baxter Permutations and Plane Bipolar Orientations

**Abstract.**
We present
a simple bijection between Baxter permutations of size *n*
and plane bipolar orientations with *n* edges. This bijection
translates several classical parameters of permutations (number of
ascents, right-to-left maxima, left-to-right
minima ...) into natural parameters of plane bipolar orientations
(number of vertices, degree of the sink, degree of the
source ...), and has remarkable symmetry properties.
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By specializing it to Baxter permutations avoiding the pattern 2413, we
obtain a bijection with non-separable planar maps.
A further specialization yields a bijection between permutations avoiding 2413 and
3142 and series-parallel maps.

Received: July 15, 2008.
Accepted: January 11, 2010.
Final Version: February 13, 2010.

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