
Schensted insertion algorithm for Young tableaux provides a
combinatorial rule for computing LittlewoodRichardson coefficients
(structure constants of grassmannians). We discuss modifications of this
algorithm which work with rcgraphs instead of Young tableaux and provide
rules for computing generalized LittlewoodRichardson coefficients
(structure constants of flag manifolds). The latest version of the
algorithm computes the coefficients $c^u_{wv}$ in the cases when v
is a grassmannian permutation, whose shape is a hook, or in the case
when v is a grassmannian permutation with the single descent at $k$ and w
is a permutation with no descents greater than $k$. The algorithm also
allows to generalize the RSK correspondence in these cases.

