关于两个和三个多边形的亏格$g$曲面的胶合
On gluing a surface of genus $g$ from two and three polygons
摘要：
本文研究了将多个多边形粘接成亏格$g$曲面的方法。本文给出了两个多边形的亏格$g$的胶合曲面数的母函数$\mathbf{C}_g^{[2]}(z)$的一个初等证明（见[4]）。此外，我们还证明了三个多边形的亏格为$g$的胶合曲面的一个类似公式。作为推论，我们已经证明了一个直接公式的数量胶合环面从三个多边形。
英文摘要：
In this paper the number of ways to glue together several polygons into a surface of genus $g$ has been investigated. We've given an elementary proof on the formula for the generating function $\mathbf{C}_g^{[2]}(z)$ of the number of gluings surface of genus $g$ from two polygons (see also [4]). Moreover, we've proven a similar formula for gluings surface of genus $g$ from three polygons. As a corollary, we've proven a direct formula for the number of gluings torus from three polygons.
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