Related papers: On Zeilberger's Constant Term for Andrews' TSSCPP …
We consider the homogeneous components U_r of the map on R = k[x,y,z]/(x^A, y^B, z^C) that multiplies by x + y + z. We prove a relationship between the Smith normal forms of submatrices of an arbitrary Toeplitz matrix using Schur…
The authors of the title proved an elegant identity expressing a Toeplitz determinant in terms of the Fredholm determinant of an infinite matrix which (although not described as such) is the product of two Hankel matrices. The proof used…
Canonical Polyadic Decomposition (CPD) represents a third-order tensor as the minimal sum of rank-1 terms. Because of its uniqueness properties the CPD has found many concrete applications in telecommunication, array processing, machine…
Zeckendorf's theorem states that every positive integer can be written uniquely as the sum of non-consecutive shifted Fibonacci numbers $\{F_n\}$, where we take $F_1=1$ and $F_2=2$. This has been generalized for any Positive Linear…
In this document, some structured operator approximation theoretical methods for system identification of nearly eventually periodic systems, are presented. Let $\mathbb{C}^{n\times m}$ denote the algebra of $n\times m$ complex matrices.…
Motivated by the telescoping proofs of two identities of Andrews and Warnaar, we find that infinite q-shifted factorials can be incorporated into the implementation of the q-Zeilberger algorithm in the approach of Chen, Hou and Mu to prove…
The structure of the set of positivity-preserving maps between matrix algebras is notoriously difficult to describe. The notable exceptions are the results by St{\o}rmer and Woronowicz from 1960s and 1970s settling the low dimensional…
Recently, we used the Sinc collocation method with the double exponential transformation to compute eigenvalues for singular Sturm-Liouville problems. In this work, we show that the computation complexity of the eigenvalues of such a…
We study the relation (and differences) between stability and Property (S) in the simple and stably finite framework. This leads us to characterize stable elements in terms of its support, and study these concepts from different sides :…
We provide geometric methods and algorithms to verify, construct and enumerate pairs of words (of specified length over a fixed $m$-letter alphabet) that form identities in the semigroup $\ut{n}$ of $n\times n$ upper triangular tropical…
Let $T$ be a matrix whose entries are linear forms over the noncommutative variables $x_1, x_2, \ldots, x_n$. The noncommutative Edmonds' problem (NSINGULAR) aims to determine whether $T$ is invertible in the free skew field generated by…
This paper introduces a framework to study discrete optimization problems which are parametric in the following sense: their constraint matrices correspond to matrices over the ring $\mathbb{Z}[x]$ of polynomials in one variable. We…
We develop a compact version of $T1$ theorem for singular integrals of Zygmund type on $\mathbb{R}^3$. More specifically, if a $(D_{\theta}, \delta_1, \delta_{2, 3})$-Calder\'{o}n-Zygmund operator $T$ associated with Zygmund dilations…
The main result of this paper is a generalization of the classical blossom algorithm for finding perfect matchings. Our algorithm can efficiently solve Boolean CSPs where each variable appears in exactly two constraints (we call it edge…
The Eigenvalue Theorem shows that solving a zero-dimensional polynomial system can be recast as an eigenvalue problem. This paper explores the relation between the Eigenvalue Theorem and the work of Ludwig Stickelberger (1850-1936).
Consider random symmetric Toeplitz matrices $T_{n}=(a_{i-j})_{i,j=1}^{n}$ with matrix entries $a_{j}, j=0,1,2,...,$ being independent real random variables such that \be \mathbb{E}[a_{j}]=0, \ \ \mathbb{E}[|a_{j}|^{2}]=1 \ \ \textrm{for}\,\…
This paper addresses the following three topics: positive semidefinite (psd) matrix completions, universal rigidity of frameworks, and the Strong Arnold Property (SAP). We show some strong connections among these topics, using semidefinite…
Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with…
Canonical Polyadic Decomposition (CPD) of a higher-order tensor is decomposition in a minimal number of rank-1 tensors. We give an overview of existing results concerning uniqueness. We present new, relaxed, conditions that guarantee…
In this paper, we focus on a special class of symmetric tensors, which can be orthogonally diagonalizable, and investigate their Z-eigenpairs problem. We show that the eigenpairs can be uniformly expressed using several basic eigenpairs,…