# Publications

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## Genus 0 characteristic numbers of tropical projective plane

Finding the so-called characteristic numbers of the complex projective plane
CP^2 is a classical
problem of enumerative geometry posed by Zeuthen more than a century ago.
For a given d and g one has to find the number of degree d genus g curves that pass through a certain generic
configuration of points and in the same time are tangent to certain generic configuration of lines. The total number
of points and lines in these two configurations is 3d-1+g so that the answer is a finite integer number.
In this paper we translate this classical problem to the corresponding enumerative problem of tropical geometry
in the case when g=0. Namely, we show that the tropical problem is well-posed and establish a special case
of the correspondence theorem that ensures that the corresponding tropical and classical numbers coincide.
Then we use the floor diagram calculus to reduce the problem to pure
combinatorics. As a consequence, we compute genus 0 characteristic
numbers of CP^2 in terms of open Hurwitz numbers.