Enumeration of multi-colored rooted maps

Anne Micheli (1) , Didier Arquès (2)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

We present a study of -colored rooted maps in orientable and locally orientable surfaces. As far as we know, no work on these maps has yet been published. We give a system of n functional equations verified by n-colored orientable rooted maps regardless of genus and with respect to edges and vertices. We exhibit the solution of this system as a vector where each component has a continued fraction form and we deduce a new equation generalizing the Dyck equation for rooted planar trees. Similar results are shown for n-colored rooted maps in locally orientable surfaces.

Mots clés: maps on any surface; dyck equation

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]

Anne Micheli, Didier Arquès. Enumeration of multi-colored rooted maps. 2000, pp.31-41. ⟨hal-00021926⟩