ON THE LOOPLESS EULERIAN VERTEX PARTITION EQUATION

Terminologies not explained here refer to [1] on enumeration, to [2, 3] on functional equations, and to [4] on combinatorial maps. Let (?) be a set of all rooted planar maps. For N∈(?); let m(N) and n(N), i≥1 represent the valency of the root-vertex and the number of non-root-vertices with valency i in N. All maps considered here are rooted loopless Eulerian planar maps. Let ? be a set of all