Grothendieck's Dessins d'Enfants in a Web of Dualities. II

Abstract

We show that the spectral curve for Eynard-Orantin topological recursions satisfied by counting Grothendieck's dessins d'enfants are related to Narayana numbers. This suggests a connection of dessins to combinatorics of Coxeter groups, noncrossing partitions, free probability theory, and cluster algebras.

References in corpus (3)

• Emergent Geometry and Mirror Symmetry of A Point
• Quantum Deformation Theory of the Airy Curve and Mirror Symmetry of a Point
• Emergent Geometry of Matrix Models with Even Couplings

Cited by in corpus (3)

• Intersection numbers on ${\overline{\mathcal{M}}}_{g,n}$ and BKP hierarchy
• Topological 1D Gravity, KP Hierarchy, and Orbifold Euler Characteristics of ${\overline{\mathcal{M}}}_{g,n}$
• On affine coordinates of the tau-function for open intersection numbers