  We show that the number of tropical curves of given genus and degree through
some given general points in the plane does not depend on the position of the
points. In the case when the degree of the curves contains only primitive
integral vectors this statement has been known for a while now, but the only
known proof was indirect with the help of Mikhalkin's Correspondence Theorem
that translates this question into the well-known fact that the numbers of
complex curves in a toric surface through some given points do not depend on
the position of the points. This paper presents a direct proof entirely within
tropical geometry that is in addition applicable to arbitrary degree of the
curves.

Algebraic Geometry