A bijection for nonorientable general maps
Jeremie Bettinelli
Laboratoire d'informatique de l'École polytechnique, Palaiseau, France
![A bijection for nonorientable general maps cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-aihpd-volume-9-issue-4.png&w=3840&q=90)
Abstract
We give a different presentation of a recent bijection due to Chapuy and Dołęga 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.
Cite this article
Jeremie Bettinelli, A bijection for nonorientable general maps. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 9 (2022), no. 4, pp. 733–791
DOI 10.4171/AIHPD/153