ID | 65998 |
FullText URL | |
Author |
Horie, Madoka
Graduate School of Science, Tohoku University
|
Abstract | Let N be a positive integer. For any positive integer L ≤ N and any positive divisor r of N, we enumerate the equivalence classes of dessins d’enfants with N edges, L faces and two vertices whose representatives have automorphism groups of order r. Further, for any non-negative integer h, we enumerate the equivalence classes of dessins with N edges, h faces of degree 2 with h ≤ N, and two vertices whose representatives have automorphism group of order r. Our arguments are essentially based upon a natural one-to-one correspondence between the equivalence classes of all dessins with N edges and the equivalence classes of all pairs of permutations whose entries generate a transitive subgroup of the symmetric group of degree N.
|
Keywords | dessin d’enfants
symmetric group
combinatorics
Riemann surface
|
Note | Mathematics Subject Classification. Primary 14H57; Secondary 05A15, 20B30.
|
Published Date | 2024-01
|
Publication Title |
Mathematical Journal of Okayama University
|
Volume | volume66
|
Issue | issue1
|
Publisher | Department of Mathematics, Faculty of Science, Okayama University
|
Start Page | 1
|
End Page | 30
|
ISSN | 0030-1566
|
NCID | AA00723502
|
Content Type |
Journal Article
|
language |
English
|
Copyright Holders | Copyright ©2024 by the Editorial Board of Mathematical Journal of Okayama University
|
File Version | publisher
|
Refereed |
True
|
Submission Path | mjou/vol66/iss1/1
|