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Mathematics > Algebraic Geometry

arXiv:1807.04197 (math)
[Submitted on 11 Jul 2018 (v1), last revised 15 Nov 2018 (this version, v2)]

Title:Cut-and-join equation for monotone Hurwitz numbers revisited

Authors:Petr Dunin-Barkowski, Reinier Kramer, Alexandr Popolitov, Sergey Shadrin
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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. Our proof in particular uses a combinatorial technique developed by Han.
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.
Comments: 7 pages. v2: Added a second proof of lemma 2.3, using Jucys-Murphy elements, and expanded motivation
Subjects: Algebraic Geometry (math.AG); Combinatorics (math.CO)
MSC classes: 14H10, 05A19, 05A18, 14Q05, 14N10, 05E05
Cite as: arXiv:1807.04197 [math.AG]
  (or arXiv:1807.04197v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1807.04197
Journal reference: J. Geom. Phys. 137 (2019), 1-6
Related DOI: https://doi.org/10.1016/j.geomphys.2018.11.010

Submission history

From: Reinier Kramer MASt MSc [view email]
[v1] Wed, 11 Jul 2018 15:33:32 UTC (13 KB)
[v2] Thu, 15 Nov 2018 08:56:40 UTC (11 KB)
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