2 citations · 2 across the 3 of their papers we have counts for
7 papers
A simple recurrence for covers of the sphere with branch points of arbitrary ramification
I. P. Goulden, Luis G. Serrano
The problem of counting ramified covers of a Riemann surface up to homeomorphism was proposed by Hurwitz in the late 1800's. This problem translates combinatorially into factoring…
An explicit form for Kerov's character polynomials
I. P. Goulden, A. Rattan
Kerov considered the normalized characters of irreducible representations of the symmetric group, evaluated on a cycle, as a polynomial in free cumulants. Biane has proved that thi…
Towards the geometry of double Hurwitz numbers
Ian Goulden, David Jackson, Ravi Vakil
Double Hurwitz numbers count branched covers of the projective line with fixed branch points, with simple branching required over all but two points 0 and infinity, and the branchi…
The Gromov-Witten potential of a point, Hurwitz numbers, and Hodge integrals
Ian Goulden, David Jackson, Ravi Vakil
Hurwitz numbers, which count certain covers of the projective line (or, equivalently, factorizations of permuations into transpositions), have been extensively studied for over a c…
The number of ramified coverings of the sphere by the double torus, and a general form for higher genera
I. P. Goulden, D. M. Jackson
An explicit expression is obtained for the generating series for the number of ramified coverings of the sphere by the double torus, with elementary branch points and prescribed ra…
The number of ramified coverings of the sphere by the torus and surfaces of higher genera
P. P. Goulden, D. M. Jackson, A. Vainshtein
We obtain an explicit expression for the number of ramified coverings of the sphere by the torus with given ramification type for a small number of ramification points, and conject…