Generalization of Schensted insertion algorithm to the cases of hooks and semi-shuffles

Given an rc-graph R of permutation w and an rc-graph Y of permutation v, we provide an insertion algorithm, which defines an rc-graph R ← Y in the case when v is a shuffle with the descent at r and w has no descents greater than r or in the case when v is a shuffle, whose shape is a hook. This algorithm gives a combinatorial rule for computing the generalized Littlewood-Richardson coefficients cwv in the two cases mentioned above.