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 ${\mathbf{C}}_g^{[2]}(z)$ 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.

Russian version published in Zap. Nauchn. Sem. POMI v.417 (2013). arXiv admin note: text overlap with arXiv:1306.2221

References in corpus (4)

• Enumeration of chord diagrams on many intervals and their non-orientable analogs
• Enumeration of linear chord diagrams
• Linear chord diagrams on two intervals
• Some formulas for the number of gluings