Name
Title | ||
|---|---|---|
Enumeration of Branched Coverings of Nonorientable Surfaces With Cyclic Branch Points |
Abstract | ||
|---|---|---|
In this paper, n-fold branched coverings of a closed nonorientable surface ${\mathcal S}$ of genus p with $r\geq 1$ cyclic branch points (that is, such that all ramification points over them are of multiplicity n) are considered. The number Np,r(n) of such coverings up to equivalence is evaluated explicitly in a closed form (without using any complicated functions such as irreducible characters of the symmetric groups). The obtained formulas depend on the parity of r and n. The method is based on some previous enumerative results and techniques for nonorientable surfaces. In particular, we generalize the approach developed for the counting of unbranched coverings of nonorientable surfaces and make use of the analytical method of roots-of-unity sums. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1137/S0895480103424043 | SIAM J. Discrete Math. |
Keywords | Field | DocType |
complicated function,closed nonorientable surface,multiplicity n,fundamental group,branched coverings,nonorientable surface,number np,permutation tuple,ramanujan sum,closed form,hurwitz number,von sterneck function,irreducible character,covering of a nonorientable surface,analytical method,genus p,nonorientable surfaces,cyclic branch point,cyclic branch points,branch point,roots of unity,symmetric group | Discrete mathematics,Combinatorics,Ramanujan's sum,Symmetric group,Enumeration,Multiplicity (mathematics),Fundamental group,Equivalence (measure theory),Ramification (botany),Mathematics,Branch point | Journal |
Volume | Issue | ISSN |
19 | 2 | 0895-4801 |
Citations | PageRank | References |
1 | 0.43 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jin Ho Kwak | 1 | 384 | 39.96 |
| Alexander Mednykh | 2 | 38 | 7.03 |
| Valery Liskovets | 3 | 5 | 1.44 |