3 papers
math-ph2020
Integrable hierarchies associated to infinite families of Frobenius manifolds
Alexey Basalaev, Petr Dunin-Barkowski, Sergey Natanzon
We propose a new construction of an integrable hierarchy associated to any infinite series of Frobenius manifolds satisfying a certain stabilization condition. We study these hiera…
math.CO2019
Combinatorics of Bousquet-Mélou-Schaeffer numbers in the light of topological recursion
Boris Bychkov, Petr Dunin-Barkowski, Sergey Shadrin
In this paper we prove, in a purely combinatorial way, a structural quasi-polynomiality property for the Bousquet-Mélou-Schaeffer numbers. Conjecturally, this property should follo…
math.AG2018
Cut-and-join equation for monotone Hurwitz numbers revisited
Petr Dunin-Barkowski, Reinier Kramer, Alexandr Popolitov +1
We give a new proof of the cut-and-join equation for the monotone Hurwitz numbers, derived first by Goulden, Guay-Paquet, and Novak. Our proof in particular uses a combinatorial te…