关键词: Map, enufuntion, functional equation, infinite matrix

Abstract:

In addition to the known method given in [1], authors provide other three
methods to the enumeration of one-vertex maps with face partition on the plane. Corre-
spondingly, there are four functional equations in the enufuntion . It is shown that the
four equations are equivalent. Moreover, an explicit expression of the solution is found by
expanding the powers of the matrix of infinite order directly.This is a new complement of
what appeared in [1].

Key words: Map, enufuntion, functional equation, infinite matrix