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MR 2827979 Reviewed Lando, S. K. Hurwitz numbers: on the edge between combinatorics and geometry. Proceedings of the International Congress of Mathematicians, volume IV, 2010, 2444--2470. (Reviewer Francesca Vetro) 14N35 (05A15 14H10 14H30 37K20)

2012
Object of study in this paper are the Hurwitz numbers. They were introduced by Hurwitz in the end of nineteenth century and still they are of great interest. The Hurwitz numbers are important in topology because they enumerate ramified coverings of two-dimensional surfaces, but not only.
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Up-down sequences

Duke Mathematical Journal, 1972
Richard Scoville
exaly  

Changes of variables in ELSV-type formulas

Michigan Mathematical Journal, 2007
Sergey Shadrin
exaly  

Graphs, quasisymmetry and permutations with restricted positions

Duke Mathematical Journal, 1974
D P Roselle
exaly  

Enumeration of permutations and sequences with restrictions

Duke Mathematical Journal, 1973
Richard Scoville
exaly  

A Dirichlet analogue of the free monogenic inverse semigroup via Möbius inversion

Rocky Mountain Journal of Mathematics, 2011
Emil Daniel Schwab
exaly  

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