On gluing a surface of genus g from two and three polygons
Abstract
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 Cg[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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