Multiplicity-free algebraic geometry is the study of subvarieties Y⊆X with the "smallest invariants" as witnessed by a multiplicity-free Chow ring decomposition of [Y] ε A-(X) into a predetermined linear basis. This paper concerns the case of Richardson subvarieties of the Grassmannian in terms of the Schubert basis. We give a nonrecursive combinatorial classification of multiplicity-free Richardson varieties, i.e., we classify multiplicity-free products of Schubert classes. This answers a question of W. Fulton.
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