26 citations · 115 across the 26 of their papers we have counts for
26 papers
Natural exact covering systems and the reversion of the Möbius series
I. P. Goulden, Andrew Granville, L. Bruce Richmond +1
We prove that the number of natural exact covering systems of cardinality is equal to the coefficient of in the reversion of the power series , w…
Asymptotics for a Class of Meandric Systems, via the Hasse Diagram of NC(n)
I. P. Goulden, Alexandru Nica, Doron Puder
We consider closed meandric systems, and their equivalent description in terms of the Hasse diagrams of the lattices of non-crossing partitions . In this equivalent descript…
On the convergence of monotone Hurwitz generating functions
I. P. Goulden, Mathieu Guay-Paquet, Jonathan Novak
Monotone Hurwitz numbers were introduced by the authors as a combinatorially natural desymmetrization of the Hurwitz numbers studied in enumerative algebraic geometry. Over the cou…
Transitive factorizations of permutations and geometry
I. P. Goulden, D. M. Jackson
We give an account of our work on transitive factorizations of permutations. The work has had impact upon other areas of mathematics such as the enumeration of graph embeddings, ra…
Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers
I. P. Goulden, Mathieu Guay-Paquet, Jonathan Novak
This article introduces mixed double Hurwitz numbers, which interpolate combinatorially between the classical double Hurwitz numbers studied by Okounkov and the monotone double Hur…
Polynomiality of monotone Hurwitz numbers in higher genera
I. P. Goulden, Mathieu Guay-Paquet, Jonathan Novak
Hurwitz numbers count branched covers of the Riemann sphere with specified ramification, or equivalently, transitive permutation factorizations in the symmetric group with specifie…