A bijection for nonorientable general maps

Jérémie Bettinelli (1)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

We give a different presentation of a recent bijection due to Chapuy and Dołega for nonorientable bipartite quadrangulations and we extend it to the case of nonorientable general maps. This can be seen as a Bouttier–Di Francesco–Guitter-like generalization of the Cori–Vauquelin– Schaeffer bijection in the context of general nonorientable surfaces. In the particular case of triangulations, the encoding objects take a particularly simple form and this allows us to recover a famous asymptotic enumeration formula found by Gao.

Mots clés: bijection; nonorientable surface; map; graph; triangulation; Brownian surface

Domaines: Combinatoire [math.CO]; Probabilités [math.PR]

Jérémie Bettinelli. A bijection for nonorientable general maps. 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), Simon Fraser University, Jul 2016, Vancouver, Canada. pp.227--238. ⟨hal-01239686v2⟩