Grothendieck's Dessins d'Enfants in a Web of Dualities. II
Jian Zhou
TL;DR
This paper explores the spectral curve associated with Grothendieck's dessins d'enfants, revealing its relation to Narayana numbers and suggesting deep connections to various combinatorial and algebraic structures.
Contribution
It establishes a link between the spectral curve of dessins d'enfants and Narayana numbers, indicating broader connections to combinatorics and algebraic theories.
Findings
Spectral curve for dessins d'enfants relates to Narayana numbers.
Connections to Coxeter groups, noncrossing partitions, and free probability.
Implications for cluster algebras and combinatorial structures.
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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory