Related papers: Kronecker products and the RSK correspondence
In this paper we consider four basic multidimensional matrix operations (outer product, Kronecker product, contraction, and projection) and two derivative operations (dot and circle products). We start with the interrelations between these…
We investigate structural properties of the binary rank of Kronecker powers of binary matrices, equivalently, the biclique partition numbers of the corresponding bipartite graphs. To this end, we engineer a Column Generation approach to…
This article aims to study some $n$-tuples of elements belonging to a ring $\mathbb{Z}/N\mathbb{Z}$ related to the combinatorics of congruence subgroups of the modular group. More precisely, we will focus here on the notion of minimal…
In this paper we propose an approach to approximate a truncated singular value decomposition of a large structured matrix. By first decomposing the matrix into a sum of Kronecker products, our approach can be used to approximate a large…
A bijection is defined from Littlewood-Richardson tableaux to rigged configurations. It is shown that this map preserves the appropriate statistics, thereby proving a quasi-particle expression for the generalized Kostka polynomials, which…
State-of-the-art embeddings often capture distinct yet complementary discriminative features: For instance, one image embedding model may excel at distinguishing fine-grained textures, while another focuses on object-level structure.…
This paper presents a new method for estimating high dimensional covariance matrices. The method, permuted rank-penalized least-squares (PRLS), is based on a Kronecker product series expansion of the true covariance matrix. Assuming an…
We analyze the decomposition problem of multivariate polynomial-exponential functions from truncated series and present new algorithms to compute their decomposition. Using the duality between polynomials and formal power series, we first…
We investigate the generalized Kronecker algebra $\mathcal{K}_r = k\Gamma_r$ with $r \geq 3$ arrows. Given a regular component $\mathcal{C}$ of the Auslander-Reiten quiver of $\mathcal{K}_r$, we show that the quasi-rank $rk(\mathcal{C}) \in…
Kronecker product kernel provides the standard approach in the kernel methods literature for learning from graph data, where edges are labeled and both start and end vertices have their own feature representations. The methods allow…
We present new proofs and generalizations of unimodality of the q-binomial coefficients \binom{n}{k}_q as polynomials in q. We use an algebraic approach by interpreting the differences between numbers of certain partitions as Kronecker…
To achieve a reliable communication with short data blocks, we propose a novel decoding strategy for Kronecker-structured constant modulus signals that provides low bit error ratios (BERs) especially in the low energy per bit to noise power…
The Kronecker product is a key algorithm and is ubiquitous across the physical, biological, and computation social sciences. Thus considerations of optimal implementation are important. The need to have high performance and computational…
A novel compressed matrix format is proposed that combines an adaptive hierarchical partitioning of the matrix with low-rank approximation. One typical application is the approximation of discretized functions on rectangular domains; the…
Traditionally, batch least squares (BLS) and recursive least squares (RLS) are used for identification of a vector of parameters that form a linear model. In some situations, however, it is of interest to identify parameters in a matrix…
In this article we study the combinatorics of congruence subgroups of the modular group. We consider the notion of minimal monomial solutions. These are the solutions of a matrix equation (also appearing in the study of Coxeter friezes),…
In this article, we study the combinatorics of congruence subgroups of the modular group. More precisely, we consider the notion of minimal monomial solutions. These are the solutions of a matrix equation (also appearing in the study of…
The relationship between linear relations and matrix pencils is investigated. Given a linear relation, we introduce its Weyr characteristic. If the linear relation is the range (or the kernel) representation of a given matrix pencil, we…
The group $SL(2,\mathbb{C})$ of all complex $2\times 2$ matrices with determinant one is closely related to the group $\boldsymbol{\mathcal{L}}_{+}^\uparrow$ of real $4\times 4$ matrices representing the restricted Lorentz transformations.…
Using an algorithm for computing the symmetric function Kronecker product of D-finite symmetric functions we find some new Kronecker product identities. The identities give closed form formulas for trace-like values of the Kronecker…