Enumeration of planar 2 - face maps 1
نویسندگان
چکیده
Up to now, most of the work on maps has dealt with rooted maps, that is, maps with a distinguished and directed edge. We get rid of this restriction in the case of planar maps having two faces. We enumerate these maps according to their vertex and face degree distributions. The following classes of non rooted 2-face maps are treated: (vertex) labelled or unlabelled, embedded in the plane or on the sphere. The motivation for this research comes from the classiication of Belyi functions. R esum e Jusqu'' a pr esent, l' etude des cartes a port e essentiellement sur les cartes point ees, c'est-a-dire ayant une ar^ ete distingu ee et orient ee. Nous levons cette restriction dans le cas des cartes a deux faces. On d enombre ces cartes selon la distribution des degr es des sommets et des faces. Les classes suivantes de cartes a deux faces non point ees sont consid er ees: etiquet ees (aux sommets) ou non, plong ees dans le plan ou sur la sph ere. La motivation de cette recherche vient de la classiication des fonctions de Belyi.
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