Relative GIT stabilities of toric Fano manifolds in low dimensions

The purpose of this paper is to clarify all the uniformly relatively Ding stable toric Fano threefolds and fourfolds as well as unstable ones. We also partially verify the relative $K$-stability of toric Fano fourfolds applying the criterion which was given in \cite{YZ16}. In the table we give the list of relative stabilities of all toric Fano fourfolds.