Geodesic
On a gluing of surfaces of genus $g$ from 2 and 3 polygons
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part VI, Tome 417 (2013), pp. 128-148 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, the number of ways to glue together several polygons into a surface of genus $g$ has been investigated. We've given an elementary proof on the formula for the generating function $\mathbf C_g^{[2]}(z)$ of the number of gluings surface of genus $g$ from two polygons (see also R. C. Penner et al. {\it Linear chord diagrams on two intervals. (2010), arXiv:1010.5857). Moreover, we've proven a similar formula for gluings surface of genus $g$ from three polygons. As a corollary, we've proven a direct formula for the number of gluings torus from three polygons. 
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A. V. Pastor. On a gluing of surfaces of genus $g$ from 2 and 3 polygons. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part VI, Tome 417 (2013), pp. 128-148. http://geodesic.mathdoc.fr/item/ZNSL_2013_417_a4/

[1] N. M. Adrianov, “Analog formuly Kharera–Tsagira dlya odnokletochnykh dvukrashennykh kart”, Funkts. analiz i ego prilozh., 31:3 (1997), 1–9 | DOI | MR | Zbl

[2] N. V. Alexeev, J. E. Andersen, R. C. Penner, P. Zograf, Enumeration of chord diagrams on many intervals and their non-orientable analogs, 2013, arXiv: 1307.0967

[3] J. E. Andersen, R. C. Penner, C. M. Reidys, M. S. Waterman, Enumeration of linear chord diagrams, 2010, arXiv: 1010.5614

[4] J. E. Andersen, R. C. Penner, C. M. Reidys, R. R. Wang, Linear chord diagrams on two intervals, 2010, arXiv: 1010.5857

[5] R. Cori, A. Machì, “Maps, hypermaps and their automorphisms: a survey. I”, Exposition. Math., 10:5 (1992), 403–427 | MR | Zbl

[6] I. P. Goulden, A. Nica, “A direct bijection for the Harer–Zagier formula”, J. Combin. Theory Ser. A, 111:2 (2005), 224–238 | DOI | MR | Zbl

[7] I. P. Goulden, W. Slofstra, “Annular embeddings of permutations for arbitrary genus”, J. Combin. Theory Ser. A, 117 (2010), 272–288 | DOI | MR | Zbl

[8] V. A. Gurvich, G. B. Shabat, “Reshenie uravneniya Kharera–Tsagira”, Uspekhi mat. nauk, 48:1 (1993), 159–160 | MR | Zbl

[9] J. Harer, D. Zagier, “The Euler characteristic of the moduli space of curves”, Inv. Math., 85:3 (1986), 457–485 | DOI | MR | Zbl

[10] A. V. Pastor, O. P. Rodionova, “Nekotorye formuly dlya chisla skleek”, Zapiski nauchn. semin. POMI, 406, 2012, 117–156 | MR