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In this paper we introduce a refined multiplicity for rational tropicalcurves in arbitrary dimension, which generalizes the refined multiplicityintroduced by F. Block and L. G\"ottsche in arXiv:1407.2901 . We then prove aninvariance statement for the count of rational tropical curves in severalenumerative problems using this new refined multiplicity. This leads to thedefinition of Block-G\"ottsche polynomials in any dimension.

Refined count for rational tropical curves in arbitrary dimension