Richardson tableaux and noncrossing partial matchings
Peter Guo
Source abstract
Richardson tableaux are a remarkable subfamily of standard Young tableaux introduced by Karp and Precup to index the irreducible components of Springer fibers equal to Richardson varieties. We prove that the set of insertion tableaux of noncrossing partial matchings on { 1 , 2 , … , n } \{1,2, \ldots , n\} by applying the Robinson–Schensted algorithm exactly coincides with the set of Richardson tableaux of size n n . This leads to a natural one-to-one correspondence between the set of Richardson tableaux of size n n and the set of Motzkin paths with n n steps, in response to a problem proposed by Karp and Precup. As applications, we recover some known properties and establish new ones for Richardson tableaux.
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