Enumeration of maps on the projective plane

The enumerative functional equation of maps by the number of inner faces, the valency of root face and the number of non-rooted vertices on the projective plane is studied. An explicit expression for the generating function by the number of inner faces and the number of non-rooted vertices is obtained. From this result, the enumeration of rooted maps by the number of edges discussed in [1] is obtained as a corollary.