Richardson tableaux are exactly the tableaux whose Springer fiber component is a Richardson variety, and they are counted by Motzkin numbers.
Consequences of the L akshmibai-- S andhya theorem: the ubiquity of permutation patterns in S chubert calculus and related geometry
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Richardson tableaux and components of Springer fibers equal to Richardson varieties
Richardson tableaux are exactly the tableaux whose Springer fiber component is a Richardson variety, and they are counted by Motzkin numbers.