160 citations · 1.4k across the 97 of their papers we have counts for
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Explicit closed algebraic formulas for Orlov-Scherbin -point functions
Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian +1
We derive a new explicit formula in terms of sums over graphs for the -point correlation functions of general formal weighted double Hurwitz numbers coming from the Kadomtsev-Pe…
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…
Half-Spin Tautological Relations and Faber's Proportionalities of Kappa Classes
Elba Garcia-Failde, Reinier Kramer, Danilo Lewański +1
We employ the -spin tautological relations to provide a particular combinatorial identity. We show that this identity is a statement equivalent to Faber's formula for proporti…
Towards an orbifold generalization of Zvonkine's -ELSV formula
Reinier Kramer, Danilo Lewanski, Alexandr Popolitov +1
We perform a key step towards the proof of Zvonkine's conjectural -ELSV formula that relates Hurwitz numbers with completed -cycles to the geometry of the moduli spaces o…
Quasi-polynomiality of monotone orbifold Hurwitz numbers and Grothendieck's dessins d'enfants
Reinier Kramer, Danilo Lewanski, Sergey Shadrin
We prove quasi-polynomiality for monotone and strictly monotone orbifold Hurwitz numbers. The second enumerative problem is also known as enumeration of a special kind of Grothendi…
On double Hurwitz numbers with completed cycles
S. Shadrin, L. Spitz, D. Zvonkine
In this paper, we collect a number of facts about double Hurwitz numbers, where the simple branch points are replaced by their more general analogues --- completed (r+1)-cycles. In…