location:  Publications → journals → CJM
Abstract view

# Transitive Factorizations in the Hyperoctahedral Group

Published:2008-04-01
Printed: Apr 2008
• G. Bini
• I. P. Goulden
• D. M. Jackson
 Format: HTML LaTeX MathJax PDF PostScript

## Abstract

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.
 MSC Classifications: 05A15 - Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 14H10 - Families, moduli (algebraic) 58D29 - Moduli problems for topological structures

 top of page | contact us | privacy | site map |