Reduced Kronecker products which are multiplicity free or contain only few components

It is known that the Kronecker coefficient of three partitions is a bounded and weakly increasing sequence if one increases the first part of all the three partitions. Furthermore, if the first parts of partitions λ , μ are big enough then the coefficients of the Kronecker product [ λ ] [ μ ] = ∑ ν g ( λ , μ , ν ) [ ν ] do not depend on the first part but only on the other parts. The reduced Kronecker product [ λ ] • ⋆ [ μ ] • can be viewed (roughly) as the Kronecker product [ ( n − | λ | , λ ) ] [ ( n − | μ | , μ ) ] for n big enough. s paper we classify the reduced Kronecker products which are multiplicity free and those which contain less than 10 components. Furthermore, we give general lower bounds for the number of constituents and components of a given reduced Kronecker product. We also give a lower bound for the number of pairs of components whose corresponding partitions differ by one box. y we argue that equality of two reduced Kronecker products is only possible in the trivial case where the factors of the products are the same.