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For a divisor $D$ on a tropical variety $X$, we define two amounts in orderto estimate the value of $h^{0}(X,D)$, which are described by terms of globalsections and computed more easily than $h^{0}(X,D)$. As an application of itsestimation, we show that a Riemann-Roch inequality holds for smooth tropicaltoric surfaces.

Riemann-Roch inequality for smooth tropical toric surfaces