We give a new proof of the cut-and-join equation for the monotone Hurwitz numbers, derived first by Goulden, Guay-Paquet, and Novak. The main interest in this particular equation is its close relation to the quadratic loop equation in the theory of spectral curve topological recursion, and we recall this motivation giving a new proof of the topological recursion for monotone Hurwitz numbers, obtained first by Do, Dyer, and Mathews.
Dunin-Barkowski, P., Kramer, R., Popolitov, A., Shadrin, S. (2019). Cut-and-join equation for monotone Hurwitz numbers revisited. JOURNAL OF GEOMETRY AND PHYSICS, 137, 1-6 [10.1016/j.geomphys.2018.11.010].
Cut-and-join equation for monotone Hurwitz numbers revisited
Kramer R.;
2019
Abstract
We give a new proof of the cut-and-join equation for the monotone Hurwitz numbers, derived first by Goulden, Guay-Paquet, and Novak. The main interest in this particular equation is its close relation to the quadratic loop equation in the theory of spectral curve topological recursion, and we recall this motivation giving a new proof of the topological recursion for monotone Hurwitz numbers, obtained first by Do, Dyer, and Mathews.
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