4 citations · 11 across the 7 of their papers we have counts for
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The KP hierarchy, branched covers, and triangulations
I. P. Goulden, D. M. Jackson
The KP hierarchy is a completely integrable system of quadratic, partial differential equations that generalizes the KdV hierarchy. A linear combination of Schur functions is a sol…
Annular embeddings of permutations for arbitrary genus
I. P. Goulden, William Slofstra
In the symmetric group on a set of size 2n, let P_{2n} denote the conjugacy class of involutions with no fixed points (equivalently, we refer to these as ``pairings'', since each d…
Enumerative Properties of NC^B(p,q)
I. P. Goulden, Alexandru Nica, Ion Oancea
We determine the rank generating function, the zeta polynomial and the Moebius function for the poset NC^B(p,q) of annular non-crossing partitions of type B, where p and q are two…
Transitive powers of Young-Jucys-Murphy elements are central
I. P. Goulden, D. M. Jackson
Although powers of the Young-Jucys-Murphya elements X_i = (1 i) + ... +(i-1 i), i = 1, ..., n, in the symmetric group S_n acting on {1, ...,n} do not lie in the centre of the group…
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…