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 generalizaztion both from a combinatorial and a geometric point of view, with the prospect of providing a mean of understanding more of the structure of the moduli spaces of maps with an 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.

G. Bini, I.P. Goulden, D.M. Jackson (2008). Transitive factorizations in the hyperoctahedral group. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 60(2), 297-312 [10.4153/CJM-2008-014-5].

Transitive factorizations in the hyperoctahedral group

G. Bini;
2008-01-01

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 generalizaztion both from a combinatorial and a geometric point of view, with the prospect of providing a mean of understanding more of the structure of the moduli spaces of maps with an 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.
Settore MAT/03 - Geometria
G. Bini, I.P. Goulden, D.M. Jackson (2008). Transitive factorizations in the hyperoctahedral group. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 60(2), 297-312 [10.4153/CJM-2008-014-5].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/398149
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