We present a study of n-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.
@article{hal-00021837,
author = {Micheli, Anne and Arqu\`es, Didier},
title = {Enumeration of multi-colored rooted maps},
journal = {HAL},
volume = {2002},
number = {0},
year = {2002},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00021837}
}
Micheli, Anne; Arquès, Didier. Enumeration of multi-colored rooted maps. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00021837/