An implicit linear description of the stable matching polytope is provided in terms of the
blocker and antiblocker sets of constraints of the matroid-kernel polytope. The explicit
identification of both these sets is based on a partition of the stable pairs in which each
agent participates. Here, we expose the relation of such a partition to rotations. We provide a
time-optimal algorithm for obtaining such a partition and establish some new related results;
most importantly, that this partition is unique.