Geodesic
Transitive Factorizations in the Hyperoctahedral Group
Canadian journal of mathematics, Tome 60 (2008) no. 2, pp. 297-312

Voir la notice de l'article provenant de la source Cambridge University Press

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 ${{\mathfrak{S}}_{2}}$ -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.
DOI : 10.4153/CJM-2008-014-5
Mots-clés : 05A15, 14H10, 58D29 
Bini, G.; Goulden, I. P.; Jackson, D. M. Transitive Factorizations in the Hyperoctahedral Group. Canadian journal of mathematics, Tome 60 (2008) no. 2, pp. 297-312. doi: 10.4153/CJM-2008-014-5
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