Geodesic
On the Tumber of Planar Maps
Canadian journal of mathematics, Tome 33 (1981) no. 1, pp. 1-11

Voir la notice de l'article provenant de la source Cambridge University Press

In a survey of methods in enumerative map theory [14], W. T. Tutte pointed out that little has been done towards enumerating unrooted maps other than plane trees. A notable exception is to be found in the work of Brown, who took the initial step in this direction by enumerating non-separable maps up to sense-preserving homeomorphisms of the plane [2]. He then took a further step, allowing sense-reversing homeomorphisms, by counting triangulations and quad-rangulations of the disc [3, 4]. In all these problems, however, there is a fixed outer region of the plane. This can be considered as a certain type of rooting of a planar map, which is normally regarded as lying on the sphere or closed plane. It is our object here to find an expression for the number of unrooted planar maps in a given set, in terms of the numbers of maps in that set which have been rooted in a special way. 
Wormald, Nicholas C. On the Tumber of Planar Maps. Canadian journal of mathematics, Tome 33 (1981) no. 1, pp. 1-11. doi: 10.4153/CJM-1981-001-6
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