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Regular version of the site

Article

Combinatorics of loop equations for branched covers of sphere

International Mathematics Research Notices. 2018. Vol. 2018. No. 18. P. 5638-5662.
Dunin-Barkowski P., Orantin N., Popolitov A., Shadrin S.

We prove, in a purely combinatorial way, the spectral curve topological recursion for the problem of enumeration of bi-colored maps, which are dual objects to dessins d'enfant. Furthermore, we give a proof of the quantum spectral curve equation for this problem. Then we consider the generalized case of 4-colored maps and outline the idea of the proof of the corresponding spectral curve topological recursion.