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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 446, Pages 139–164 (Mi znsl6287)  
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
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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.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-07906
Ministry of Education and Science of the Russian Federation 14.Z50.31.0020
Matej Bel University 26110230082
Czech Ministry of Education, Youth and Sports LO1506
Slovak Ministry of Education, Research and Sports VEGA 1/0150/14
The research of the first author was partially supported by the Russian Foundation for Basic Research (grant 15-01-07906) and Laboratory of Quantum Topology, Chelyabinsk State University, Russian Federation government grant no. 14.Z50.31.0020. Both authors were supported by the project “Mobility-Enhancing Research, Science and Education”, Matej Bel University (ITMS code 26110230082) under the Operational Programme of Education cofinanced by the European Social Foundation. The second author was supported by the project LO1506 of the Czech Ministry of Education, Youth and Sports, and by the project VEGA 1/0150/14 of the Slovak Ministry of Education, Research and Sports.
Received: 23.03.2016
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 226, Issue 5, Pages 635–654
DOI: https://doi.org/10.1007/s10958-017-3555-5
Bibliographic databases:
Document Type: Article
UDC: 519.175.3+525.162.6
Language: English
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
Citation in format AMSBIB
\Bibitem{MedNed16}
\by A.~Mednykh, R.~Nedela
\paper Recent progress in enumeration of hypermaps
\inbook Combinatorics and graph theory. Part~V
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 446
\pages 139--164
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6287}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3520426}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 226
\issue 5
\pages 635--654
\crossref{https://doi.org/10.1007/s10958-017-3555-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85029694077}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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