Geodesic
Simple Hurwitz Numbers of a Disk
Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 1, pp. 44-58

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Let $D$ be the closed unit disk. We study the Hurwitz numbers corresponding to the coverings of $D$ whose only multiple critical value lies on the boundary of $D$ and find differential equations describing the generating function of these numbers.
Keywords: Hurwitz numbers, topological field theory, cut-and-join equation. 
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     author = {S. M. Natanzon},
     title = {Simple {Hurwitz} {Numbers} of a {Disk}},
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S. M. Natanzon. Simple Hurwitz Numbers of a Disk. Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 1, pp. 44-58. http://geodesic.mathdoc.fr/item/FAA_2010_44_1_a3/