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A Proof of a Conjecture for the Number of Ramified Coverings of the Sphere by the Torus

✍ Scribed by I.P. Goulden; D.M. Jackson

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 136 KB
Volume: 88
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1999.2992

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✦ Synopsis

An explicit expression is obtained for the generating series for the number of ramified coverings of the sphere by the torus, with elementary branch points and prescribed ramification type over infinity. This proves a conjecture of Goulden, Jackson, and Vainshtein for the explicit number of such coverings.

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