  Hurwitz numbers count genus g, degree d covers of the projective line with
fixed branch locus. This equals the degree of a natural branch map defined on
the Hurwitz space. In tropical geometry, algebraic curves are replaced by
certain piece-wise linear objects called tropical curves. This paper develops a
tropical counterpart of the branch map and shows that its degree recovers
classical Hurwitz numbers.

Algebraic Geometry;Combinatorics