Baxter permutations and plane bipolar orientations

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.

• Type: Journal
• Year: 2008
• Where: ENDM
• Authors: Nicolas Bonichon, Mireille Bousquet-Mélou, Éric Fusy
• Keywords: Baxter Permutations, ENDM 2008, Permutations, Plane Bipolar Orientations