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

TL;DR

This paper determines the automorphism groups of tropical moduli spaces of genus zero curves, showing they are isomorphic to symmetric groups depending on the number of marked points.

Contribution

It establishes the automorphism groups of tropical moduli spaces as symmetric groups, extending understanding of their symmetries for different n.

Findings

Automorphism groups of $M_{0,n}^{ ext{trop}}$ and $ar{M}_{0,n}^{ ext{trop}}$ are isomorphic to $S_n$ for $n extgreater=5$.

For $n=4$, the automorphism groups are isomorphic to $S_3$.

Results clarify the symmetry structure of tropical moduli spaces.

Abstract

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 $S_3$.