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.
Publié le : 2000-07-05
Classification:
maps on any surface,
dyck equation,
[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],
[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
@article{hal-00021926,
author = {Micheli, Anne and Arqu\`es, Didier},
title = {Enumeration of multi-colored rooted maps},
journal = {HAL},
volume = {2000},
number = {0},
year = {2000},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00021926}
}
Micheli, Anne; Arquès, Didier. Enumeration of multi-colored rooted maps. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00021926/