Explicit enumeration of triangulations with multiple boundaries

Maxim Krikun (1)

1 IECN - Institut Élie Cartan de Nancy

We enumerate rooted triangulations of a sphere with multiple holes by the total number of edges and the length of each boundary component. The proof relies on a combinatorial identity due to W.T. Tutte.

Mots clés: planar maps; triangulation; loop equation

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

Maxim Krikun. Explicit enumeration of triangulations with multiple boundaries. The Electronic Journal of Combinatorics, 2007, 14 (1), pp.R61. ⟨10.48550/arXiv.0706.0681⟩. ⟨hal-00151870v2⟩