Geodesic
Baxter Permutations and Plane Bipolar Orientations
Séminaire lotharingien de combinatoire, 61A (2009-2011)

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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. % 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. 

@article{SLC_2009-2011_61A_a7,
     author = {Nicolas Bonichon and Mireille Bousquet-M\'elou and \'Eric Fusy},
     title = {Baxter {Permutations} and {Plane} {Bipolar} {Orientations}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {61A},
     year = {2009-2011},
     url = {http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a7/}
}
TY  - JOUR
AU  - Nicolas Bonichon
AU  - Mireille Bousquet-Mélou
AU  - Éric Fusy
TI  - Baxter Permutations and Plane Bipolar Orientations
JO  - Séminaire lotharingien de combinatoire
PY  - 2009-2011
VL  - 61A
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a7/
ID  - SLC_2009-2011_61A_a7
ER  - 
%0 Journal Article
%A Nicolas Bonichon
%A Mireille Bousquet-Mélou
%A Éric Fusy
%T Baxter Permutations and Plane Bipolar Orientations
%J Séminaire lotharingien de combinatoire
%D 2009-2011
%V 61A
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a7/
%F SLC_2009-2011_61A_a7
Nicolas Bonichon; Mireille Bousquet-Mélou; Éric Fusy. Baxter Permutations and Plane Bipolar Orientations. Séminaire lotharingien de combinatoire, 61A (2009-2011). http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a7/