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.
Transitive factorizations in the hyperoctahedral group / G. Bini, I.P. Goulden, D.M. Jackson. - In: CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES. - ISSN 0008-414X. - 60:2(2008), pp. 297-312. [10.4153/CJM-2008-014-5]
Transitive factorizations in the hyperoctahedral group
G. BiniPrimo
;
2008
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.Pubblicazioni consigliate
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