  The aim of this paper is to discuss a combinatorial characterisation of
stability for toric vector bundles (or equivariant reflexive sheaves) in the
terms of their parliaments of polytopes, a generalization of moment polytopes
for toric vector bundles by Di Rocco, Jabbusch and Smith. We also define
subparliaments of polytopes and identify them with parliaments of equivariant
subbundles.
