asymptotic expression
1.Abstract: This paper provides the functional equation of general rooted maps with the number of inner faces, the rooted face valency and the number of non-rooted vertices as parameters on the torus, and gives an explicit expression of the enumerating function of these maps with the number of inner faces and of non-rooted vertices, then the number of these maps with the size as a parameter whose asymptotic result had been obtained in [2] is obtained as a corollary.
2.This paper provides the functional equation of general rooted maps with the number of inner faces, the rooted face valency and the number of non-rooted vertices as parameters on the torus, and gives an explicit expression of the enumerating function of these maps with the number of inner faces and of non-rooted vertices, then the number of these maps with the size as a parameter whose asymptotic result had been obtained in [2] is obtained as a corollary.
