Gluings of surfaces with polygonal boundaries
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By pairwise gluing edges of a polygon, one obtains two-dimensional surfaces with handles and holes. We compute the number N g,L (n 1, ..., n L ) of distinct ways to obtain a surface of given genus g whose boundary consists of L polygonal components with given numbers n 1, ..., n L of edges. Using combinatorial relations between graphs on real two-dimensional surfaces, we derive recursion relations between the N g,L . We show that the Harer-Zagier numbers arise as a special case of N g,L and derive a new closed-form expression for them.
Key wordsgraph on surface number of graphs generating function
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