Using a modification found by Vallejo and Avella of the RSK algorithm, it is possible to describe a Kronecker product χλ⊗χμ⊗χν when ν is a two-part partition as a difference of the number of integral points contained on some sections of a family of polytopes.

These polytopes, having very high dimension and a large number of defining hyperplanes can be described by conventional geometric means only in the simplest cases. However using ideas from matroid theory, a method is developed to generate polytope vertices in the general case