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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 446, Pages 139–164
(Mi znsl6287)
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This article is cited in 1 scientific paper (total in 1 paper)
Recent progress in enumeration of hypermaps
A. Mednykhabc, R. Nedelade a Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia
b Chelyabinsk State University, 454001 Chelyabinsk, Russia
c Novosibirsk State University, 630090 Novosibirsk, Russia
d NTIS New Technologies for Information Society, Faculty of Applied Sciences, University of West Bohemia, Technická8, 306 14 Plzeň, Czech Republic
e Matej Bel University, Slovak Republic
Abstract:
We enumerate the isomorphism classes of hypermaps of a given genus $g\le6$ and a given number of darts $d$. The hypermaps of a given genus $g$ are distinguished up to orientation preserving isomorphisms. Our results depend on recent progress in counting rooted hypermaps, in particular by P. Zograf, M. Kazarian, A. Giorgetti and T. Walsh. These results can be interpreted as an enumeration of conjugacy classes of subgroups of the free Fuchsian group of rank two with a genus restriction.
Key words and phrases:
enumeration, map, surface, orbifold, rooted hypermap, unrooted hypermap, Fuchsian group.
Received: 23.03.2016
Citation:
A. Mednykh, R. Nedela, “Recent progress in enumeration of hypermaps”, Combinatorics and graph theory. Part V, Zap. Nauchn. Sem. POMI, 446, POMI, St. Petersburg, 2016, 139–164; J. Math. Sci. (N. Y.), 226:5 (2017), 635–654
Linking options:
https://www.mathnet.ru/eng/znsl6287 https://www.mathnet.ru/eng/znsl/v446/p139
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Abstract page: | 241 | Full-text PDF : | 81 | References: | 62 |
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