Related papers: Kronecker products and the RSK correspondence
The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…
We study analogues of Kronecker coefficients for symmetric inverse semigroups, for dual symmetric inverse semigroups and for the inverse semigroups of bijections between subquotients of finite sets. In all cases we reduce the problem of…
Utilizing spectral residues of parameterized, recursively defined sequences, we develop a general method for generating identities of composition sums. Specific results are obtained by focusing on coefficient sequences of solutions of first…
We propose a new approach to study the Kronecker coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. We explain the limiting behavior and associated bounds in the context of the partition…
The problem of polynomial regression in which the usual monomial basis is replaced by the Bernstein basis is considered. The coefficient matrix A of the overdetermined system to be solved in the least squares sense is then a rectangular…
Let $\mathbb{k}$ be an algebraically closed field. Connections between representations of the generalized Kronecker quivers $K_r$ and vector bundles on $\mathbb{P}^{r-1}$ have been known for quite some time. This article is concerned with a…
Comparative analyses of graph structured datasets underly diverse problems. Examples of these problems include identification of conserved functional components (biochemical interactions) across species, structural similarity of large…
In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…
We propose a novel Riemannian manifold preconditioning approach for the tensor completion problem with rank constraint. A novel Riemannian metric or inner product is proposed that exploits the least-squares structure of the cost function…
Linear recurrent sequences are those whose elements are defined as linear combinations of preceding elements, and finding recurrence relations is a fundamental problem in computer algebra. In this paper, we focus on sequences whose elements…
Kronecker coefficients encode the tensor products of complex irreducible representations of symmetric groups. Their stability properties have been considered recently by several authors (Vallejo, Pak and Panova, Stembridge). We describe a…
A Robinson similarity matrix is a symmetric matrix where the entry values on all rows and columns increase toward the diagonal. Decompose the Robinson matrix into the sum of k {0, 1}-matrices, then these k {0, 1}-matrices are the adjacency…
Multidimensional NMR inversion using Kronecker products poses several challenges. First, kernel compression is only possible when the kernel matrices are separable, and in recent years, there has been an increasing interest in NMR sequences…
We introduce an algorithm to decompose orthogonal matrix representations of the symmetric group over the reals into irreducible representations, which as a by-product also computes the multiplicities of the irreducible representations. The…
Differentiable systems in this paper means systems of equations that are described by differentiable real functions in real matrix variables. This paper proposes algorithms for finding minimal rank solutions to such systems over (arbitrary…
The Kronecker product of two Schur functions $s_{\mu}$ and $s_{\nu}$, denoted by $s_{\mu}*s_{\nu}$, is the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group corresponding to the…
Brualdi and Ma found a connection between involutions of length $n$ with $k$ descents and symmetric $k\times k$ matrices with non-negative integer entries summing to $n$ and having no row or column of zeros. From their main theorem they…
Can one recover a matrix efficiently from only matrix-vector products? If so, how many are needed? This paper describes algorithms to recover matrices with known structures, such as tridiagonal, Toeplitz, Toeplitz-like, and hierarchical…
We present a number of combinatorial characterizations of K-matrices. This extends a theorem of Fiedler and Ptak on linear-algebraic characterizations of K-matrices to the setting of oriented matroids. Our proof is elementary and simplifies…
We study the matrix-variate regression problem $Y_i = \sum_{k} \beta_{1k} X_i \beta_{2k}^{\top} + E_i$ for $i=1,2\dots,n$ in the high dimensional regime wherein the response $Y_i$ are matrices whose dimensions $p_{1}\times p_{2}$ outgrow…