Gluings of surfaces with polygonal boundaries



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 words

graph on surface number of graphs generating function 


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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Institute for Theoretical and Experimental PhysicsMoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyMoscowRussia

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