# Generalised ordinary vs fully simple duality for $n$-point functions and a proof of the Borot--Garcia-Failde conjecture

@inproceedings{Bychkov2021GeneralisedOV, title={Generalised ordinary vs fully simple duality for \$n\$-point functions and a proof of the Borot--Garcia-Failde conjecture}, author={B. Bychkov and P. Dunin-Barkowski and M. Kazarian and S. Shadrin}, year={2021} }

We study a duality for the n-point functions in VEV formalism that we call the ordinary vs fully simple duality. It provides an ultimate generalisation and a proper context for the duality between maps and fully simple maps observed by Borot and Garcia-Failde. Our approach allows to transfer the algebraicity properties between the systems of n-point functions related by this duality, and gives direct tools for the analysis of singularities. As an application, we give a proof of a recent… Expand

#### One Citation

Explicit closed algebraic formulas for Orlov-Scherbin $n$-point functions

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We derive a new explicit formula in terms of sums over graphs for the npoint correlation functions of general formal weighted double Hurwitz numbers coming from the Orlov–Scherbin partition… Expand

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