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In this paper we show that the automorphism groups of $M_{0,n}^{\text{trop}}$and $\overline{M}_{0,n}^{\text{trop}}$ are isomorphic to the permutation group$S_n$ for $n\geq5$, while the automorphism groups of $M_{0,4}^{\text{trop}}$and $\overline{M}_{0,4}^{\text{trop}}$ are isomorphic to the permutation group$S_3$.

The automorphism group of $M_{0,n}^\text{trop}$ and $\overline{M}_{0,n}^{\text{trop}}$