Transitive Factorizations in the Hyperoctahedral Group
Printed: Apr 2008
I. P. Goulden
D. M. Jackson
The classical Hurwitz enumeration problem has a presentation in terms of
transitive factorizations in the symmetric group. This presentation suggests
a generalization from type~$A$ to other
finite reflection groups and, in particular, to type~$B$.
We study this generalization both from a combinatorial and a geometric
point of view, with the prospect of providing a means of understanding more
of the structure of the moduli spaces of maps with an $\gS_2$-symmetry.
The type~$A$ case has been well studied and connects Hurwitz numbers
to the moduli space of curves. We conjecture an analogous setting for the
type~$B$ case that is studied here.
05A15 - Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]
14H10 - Families, moduli (algebraic)
58D29 - Moduli problems for topological structures