Gr\"obner fans of Specht ideals

In this paper, we give the Gr"obner fan and the state polytope of a Specht ideal $I_{\lambda }$ explicitly. In particular, we show that the state polytope of $I_{\lambda }$ for a partition $\lambda =({\lambda }_1,\dots ,{\lambda }_m)$ is always a generalized permutohedron, and it is a (usual) permutohedron if and only if ${\lambda }_{i-1}={\lambda }_i>0$ for some $i$.