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The Gluing of a Surface of Genus g from Two and Three Polygons

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In this paper, the number of ways for gluing together several polygons into a surface of genus g is investigated. An elementary proof of the formula for the generating function \( {\mathrm{C}}_{\mathfrak{g}}^{\left[2\right]}(z) \) of the number of gluings of a surface of genus g from two polygons is given. Moreover, a similar formula is proved for gluings of a surface of genus g from three polygons. As a consequence, a direct formula is obtained for the number of gluings of a torus from three polygons. Bibliography: 10 titles.

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Authors and Affiliations

  1. St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg State Polytechnical University, St. Petersburg, Russia

    A. V. Pastor

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  1. A. V. Pastor
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Correspondence to A. V. Pastor.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 417, 2013, pp. 128–148.

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Pastor, A.V. The Gluing of a Surface of Genus g from Two and Three Polygons. J Math Sci 204, 258–270 (2015). https://doi.org/10.1007/s10958-014-2200-9

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  • DOI: https://doi.org/10.1007/s10958-014-2200-9

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