A proof of a conjecture for the number of ramified coverings of the sphere by the torus

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78035An 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.10 pagesAlgebraic GeometryCombinatorics5*D29, 58C35, 05C30, 05E05A proof of a conjecture for the number of ramified coverings of the sphere by the torustext