51 citations · 202 across the 15 of their papers we have counts for
16 papers
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…
A second proof of the Shareshian--Wachs conjecture, by way of a new Hopf algebra
Mathieu Guay-Paquet
This is a set of working notes which give a second proof of the Shareshian--Wachs conjecture, the first (and recent) proof being by Brosnan and Chow in November 2015. The conjectur…
The combinatorics of real double Hurwitz numbers with real positive branch points
Mathieu Guay-Paquet, Hannah Markwig, Johannes Rau
We investigate the combinatorics of real double Hurwitz numbers with real positive branch points using the symmetric group. Our main focus is twofold. First, we prove correspondenc…
Generating functions for weighted Hurwitz numbers
Mathieu Guay-Paquet, J. Harnad
Double Hurwitz numbers enumerating weighted -sheeted branched coverings of the Riemann sphere or, equivalently, weighted paths in the Cayley graph of generated by transpos…
Star-cumulants of free unitary Brownian motion
Nizar Demni, Mathieu Guay-Paquet, Alexandru Nica
We study joint free cumulants of u_t and u_t^{*}, where u_t is a free unitary Brownian motion at time t. We determine explicitly some special families of such cumulants. On the oth…
2D Toda τ-functions as combinatorial generating functions
Mathieu Guay-Paquet, J. Harnad
Two methods of constructing 2D Toda -functions that are generating functions for certain geometrical invariants of a combinatorial nature are related. The first involves generat…