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Floor decompositions of tropical curves in any dimension

We reduce the computation of Gromov-Witten invariants of CP^n in genus 0 to the combinatorial enumeration of floor diagrams. This formula was announced in \cite{Br7}.
This is a preliminary draft of the extended version of \cite{Br7}. The final version of the paper will also contain the computation of Welschinger invariants of RP^3, and will be available soon.