  Young's lattice is a prototypical example of differential posets.
Differential posets have the Robinson correspondence, the correspondence
between permutations and pairs of standard tableaux with the same shape, as in
the case of Young's lattice. Fomin introduced generalized Schur operators to
generalize the method of Robinson correspondence in differential posets to the
Robinson-Schensted-Knuth correspondence, the correspondence between certain
matrices and pairs of semi-standard tableaux with the same shape. In this
paper, we introduce operators on the vector space whose basis is the set of
planar binary trees. To prove that the operators are generalized Schur
operators, we construct a correspondence, which is an extension of Fomin's
r-correspondence for them.
