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math.CO2005
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…
math.CO2005
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…