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The character theoretic approach [5] to the enumeration of rooted maps in an orientable surface of arbitrary genus is extended to 2-face-colorable rooted maps. In particular, we show that there exists, for each genus, a correspondence between the set of 2-colored triangulations and a set of 2-colored rooted maps of all lower genera with a distinguished subset of vertices.

Character theory and rooted maps in an orientable surface of given genus: face-colored maps