In type A, positive Minkowski sum of Schubert-matroid MV polytopes yields an MV polytope precisely when the indexing family is weakly separated.
Danilov, Gleb A
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Stability of Type A Mirkovi\'c-Vilonen Polytopes under Minkowski Sum via Weak Separation
In type A, positive Minkowski sum of Schubert-matroid MV polytopes yields an MV polytope precisely when the indexing family is weakly separated.