曲面四角化上的直差分方程

A Straight Difference Equation on Surface Quadrangulations

本文旨在讨论由球面(或平面)近四角化以度和根面次为参数根同构类引出的函数方程.论证了在整域扩张中解的存在性和唯一性.而且,也导出了这个解的正项和表示式.在此基础上,引进欠-1面四角化,通过讨论以度、欠面次和根面次为参数根同构类,得到一个三变元函数的直差分方程,进而导致在泛柱面上的情形,也求出解的正项和表示式.

The purpose of this paper is to investigate a functional equation arising from counting rooted isomor- phic classes of near quadrangulations on the sphere with two parameters ： the size and the root - face valency by determining the well -definedness on the extension of integral domain. A summation form of the solution with all terms positive is provided. On this basis, Mis-1 face near difference equation for counting rooted isomorphic classes quadrangulations are introduced. A system of straight of mis-1 near quadrangulations on the pancylinder（ a surface with two boundaries） with three parameters ： the size, the root - face valency and the valency of mis - face is found. The well - definedness and a summation form with all terms positive of the solution are also done in the extension of integral domain.