We present combinatorial operators for the expansion of the Kronecker product of irreducible representations of the symmetric group Sn. These combinatorial operators are defined in the ring of symmetric functions and act on the Schur functions basis. This leads to a combinatorial description of the Kronecker powers of the irreducible representations indexed with the partition (n − 1, 1) which s...

This paper gives an overview of notations used in multiway array processing. We redefine the vectorization and matricization operators to comply with some properties of the Kronecker product. The tensor product and Kronecker product are also represented with two different symbols, and it is shown how these notations lead to clearer expressions for multiway array operations. Finally, the paper r...

Proof. One can relate the singular values of the Hadamard product Z 2 to those of the Kronecker product Z ⊗ Z. In particular, as Z Z can be obtain from Z ⊗ Z by deleting some rows and columns, Lemma A.1 tells us that σmin(Z Z) ≥ σmin(Z ⊗ Z) and σmax(Z Z) ≤ σmax(Z ⊗ Z). Then the lemma follows as the Kronecker product Z⊗Z is known to have the property that σmin(Z⊗ Z) = (σmin(Z)) 2 and σmax(Z ⊗ Z)...

In this letter, a sparse Kronecker-product (SKP) coding scheme is proposed for unsourced multiple access. Specifically, the data of each active user encoded as Kronecker product two component codewords with one being and other forward-error-correction (FEC) coded. At receiver, an iterative decoding algorithm developed, consisting matrix factorization decomposition soft-in soft-out code FEC code...