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This article is cited in 8 scientific papers (total in 8 papers)
Gluings of Surfaces with Polygonal Boundaries
E. T. Akhmedovab, Sh. R. Shakirovab a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b Moscow Institute of Physics and Technology
Abstract:
By pairwise gluing edges of a polygon, one obtains two-dimensional surfaces with handles and holes. We compute the number $\mathcal{N}_{g,L}(n_1,\dots,n_L)$ of distinct ways to obtain a surface of given genus $g$ whose boundary consists of $L$ polygonal components with given numbers $n_1,\dots,n_L$ of edges. Using combinatorial relations between graphs on real two-dimensional surfaces, we derive recursion relations between the $\mathcal{N}_{g,L}$. We show that the Harer–Zagier numbers arise as a special case of $\mathcal{N}_{g,L}$ and derive a new closed-form expression for them.
Keywords:
graph on surface, number of graphs, generating function.
Received: 17.12.2007
Citation:
E. T. Akhmedov, Sh. R. Shakirov, “Gluings of Surfaces with Polygonal Boundaries”, Funktsional. Anal. i Prilozhen., 43:4 (2009), 3–13; Funct. Anal. Appl., 43:4 (2009), 245–253
Linking options:
https://www.mathnet.ru/eng/faa2968https://doi.org/10.4213/faa2968 https://www.mathnet.ru/eng/faa/v43/i4/p3
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Abstract page: | 509 | Full-text PDF : | 371 | References: | 49 | First page: | 21 |
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