Email this article Recent Progress in Enumeration of Hypermaps
- Authors: Mednykh A.1,2,3, Nedela R.4,5
-
Affiliations:
- Sobolev Institute of Mathematics
- Novosibirsk State University
- Chelyabinsk State University
- University of West Bohemia
- Matej Bel University
- Issue: Vol 226, No 5 (2017)
- Pages: 635-654
- Section: Article
- URL: https://journal-vniispk.ru/1072-3374/article/view/240041
- DOI: https://doi.org/10.1007/s10958-017-3555-5
- ID: 240041
Cite item
Open Access
Access granted
Subscription Access
Abstract
The isomorphism classes of hypermaps of a given genus g ≤ 6 and a given number d of darts are enumerated. The hypermaps of a given genus g are distinguished up to orientation preserving isomorphisms. The obtained 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 in a free Fuchsian group of rank two with a genus restriction. Bibliography: 36 titles.
About the authors
A. Mednykh
Sobolev Institute of Mathematics; Novosibirsk State University; Chelyabinsk State University
Author for correspondence.
Email: mednykh@math.nsc.ru
Russian Federation, Novosibirsk; Novosibirsk; Chelyabinsk
R. Nedela
University of West Bohemia; Matej Bel University
Email: mednykh@math.nsc.ru
Czech Republic, Plzeň; Banská Bystrica
Supplementary files
