Geodesic
Some formulas for the number of gluings
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part V, Tome 406 (2012), pp. 117-156

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In this paper the number of ways to glue a surface of genus $g$ has been investigated. We've proven formulas for the number of gluings sphere from three polygons and from two bicolored polygons. Moreover, we've given a new proofs on the formulas for the number of gluings sphere and torus from two polygons. 
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     author = {A. V. Pastor and O. P. Rodionova},
     title = {Some formulas for the number of gluings},
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     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_406_a6/}
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A. V. Pastor; O. P. Rodionova. Some formulas for the number of gluings. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part V, Tome 406 (2012), pp. 117-156. http://geodesic.mathdoc.fr/item/ZNSL_2012_406_a6/