Tropical hyperplane arrangements and combinatorial mutations of the matching field polytopes of Grassmannians

A sequence of combinatorial mutations of matching field polytopes preserves the property of giving rise to a toric degeneration of Grassmannians. In this paper, we find a way to check that two matching field polytopes are combinatorial mutation equivalence using tropical hyperplane arrangements, ``literally at a glance". Our way can prove that block diagonal matching fields are combinatorial mutations equivalent to diagonal matching fields. This is one of main results in clarke2021combinatorial. Our result can be regarded as a generalization of that result.