We give formulae for computing Kronecker coefficients occurring in the expansion of sμ ∗ sν , where both μ and ν are nearly rectangular, and have smallest parts equal to either 1 or 2. In particular, we study s(n,n−1,1) ∗ s(n,n), s(n−1,n−1,1) ∗ s(n,n−1), s(n−1,n−1,2) ∗ s(n,n), s(n−1,n−1,1,1) ∗ s(n,n) and s(n,n,1) ∗ s(n,n,1). Our approach relies on the interplay between manipulation of symmetric...

Kronecker coefficients are the multiplicities in the tensor product decomposition of two irreducible representations of the symmetric group Sn. They can also be interpreted as the coefficients of the expansion of the internal product of two Schur polynomials in the basis of Schur polynomials. We show that the problem KRONCOEFF of computing Kronecker coefficients is very difficult. More specific...

We describe an interface and an implementation for performing Kronecker product actions on NVIDIA GPUs for multiple small 2-D matrices and 3-D arrays processed in parallel as a batch. This method is suited to cases where the Kronecker product component matrices are identical but the operands in a matrix-free application vary in the batch. Any batched GEMM (General Matrix Multiply) implementatio...

The multilinear system framework allows for the exploitation of identification problem from different perspectives in context various applications, such as nonlinear acoustic echo cancellation, multi-party audio conferencing, and video which could be modeled through parallel or cascaded filters. In this paper, we introduce memoryless memory structures that are described a bilinear perspective. ...

The tensor product, also called direct, categorical, or Kronecker product of graphs, is one of the least-understood graph products. In this paper we determine partial answers to the question given in the title, thereby significantly extending results of Broere and Hattingh (see [2]). We characterize completely those pairs of complete graphs whose tensor products are circulant. We establish that...