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Goulden, Jackson and Vakil observed a polynomial structure underlying one-part double Hurwitz numbers, which enumerate branched covers of $\mathbb{CP}^1$ with prescribed ramification profile over $\infty$, a unique preimage over 0, and simple branching elsewhere.
Loop equations and a proof of Zvonkine’s q r qr -ELSV formula
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Equivalence of ELSV and Bouchard-Mariño conjectures for r r -spin Hurwitz numbers
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Special cases of the orbifold version of Zvonkine’s r r -ELSV formula
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Ueber Riemann’sche Flächen mit gegebenen Verzweigungspunkten
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Double ramification cycles on the moduli spaces of curves
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Chiodo formulas for the r r -th roots and topological recursion
Danilo Lewanski, Alexandr Popolitov, Sergey Shadrin, and Dimitri Zvonkine · 2017
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Towards an orbifold generalization of Zvonkine’s r r -ELSV formula
R. Kramer, D. Lewanski, A. Popolitov, and S. Shadrin · 2019
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