51 citations · 202 across the 15 of their papers we have counts for
5 papers · 1 filter
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…
The generating function for total displacement
T. Kyle Petersen, Mathieu Guay-Paquet
In a 1977 paper, Diaconis and Graham studied what Knuth calls the total displacement of a permutation , which is the sum of the distances . In recent work of the first…