无环有根平面地图节点剖分计数方程

Enumerial Equation of Rooted No-Loop Plane Maps with Vertex Partition

本文对无环有根平面地图进行了研究,得到了它的节点剖分计数方程:D=1+_y^(-1)((xy6_(x,y)D)/(1-xy6_(x,y)D)(D=D(x,y_1,y_2……),6_(x,y)D=(xD-yD(y))/(x-y),D(y)=D(y_1,y_2,……),_y(y_i)=y^i );通过运用作者建立的设立参数法得到了它的以根节点度数、边数以及节点个数为计数参数的二次计数方程:X^2YF^2+[-Z(X-1)-XYF(1)+X^2YZ^2-X^2Y]·F+Z^2(X-1)+XYZF(1)-XYZ^2F(1)=0 (F=F(X,Y,Z),F(1)=F(1,Y,Z)),并求得它的仅以边数为计数参数的计数显式解(6(4n+1)!)/((3n+3)!n!).

In this paper, the author made the research to rooted no-loop plane maps and obtained its enumerial equation with vertex partition D = l+ by applying the method of 'Making-parmeters Method' established by the author, the author obtained its enumeral equation with rooted vertice degrees, edges and rertices X2YF+ [-Z (X-1) -XYF(1)+X2YZ2-X2Y] .F + Z2 (X- 1) + XYZF(1)-XYZ2F(1) = 0, the author also obtained its enumeral solution with edges