Spectral curve for Eynard-Orantin recursions on dessins d'enfants is related to Narayana numbers.
Emergent Geometry of Matrix Models with Even Couplings
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abstract
We show that to the modified GUE partition function with even coupling introduced by Dubrovin, Liu, Yang and Zhang, one can associate $n$-point correlation functions in arbitrary genera which satisfy Eynard-Orantin topological recursions. Furthermore, these $n$-point functions are related to intersection numbers on the Deligne-Mumford moduli spaces.
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2019 1verdicts
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Grothendieck's Dessins d'Enfants in a Web of Dualities. II
Spectral curve for Eynard-Orantin recursions on dessins d'enfants is related to Narayana numbers.