5 papers
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…
The twisting procedure
Vladimir Dotsenko, Sergey Shadrin, Bruno Vallette
This paper provides a conceptual study of the twisting procedure, which amounts to create functorially new differential graded Lie algebras, associative algebras or operads (as wel…
Ground states of Nicolai and Nicolai models
Ruben La, Kareljan Schoutens, Sergey Shadrin
We derive explicit recursions for the ground state generating functions of the one-dimensional Nicolai model and Nicolai model. Both are examples of lattice models w…
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…