Related papers: Vertically symmetric alternating sign matrices and…
Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…
Alternating sign trapezoids have recently been introduced as a generalisation of alternating sign triangles. Fischer established a threefold refined enumeration of alternating sign trapezoids and provided three statistics on column strict…
This work explores the tensor and combinatorial constructs underlying the linearised higher-order variational equations of a generic autonomous system along a particular solution. The main result of this paper is a compact yet explicit and…
In this paper, we consider the problem of representing a multivariate polynomial as the determinant of a definite (monic) symmetric/Hermitian linear matrix polynomial (LMP). Such a polynomial is known as determinantal polynomial.…
In this paper, we use two-variable Laurent polynomials attached to matrices to encode properties of compositions of sequences. The Lagrange identity in the ring of Laurent polynomials is then used to give a short and transparent proof of a…
This article focuses on the problem of reconstructing low-rank matrices from underdetermined measurements using alternating optimization strategies. We endeavour to combine an alternating least-squares based estimation strategy with ideas…
A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…
We initiate a study of the zero-nonzero patterns of n by n alternating sign matrices. We characterize the row (column) sum vectors of these patterns and determine their minimum term rank. In the case of connected alternating sign matrices,…
Fischer provided a new type of binomial determinant for the number of alternating sign matrices involving the third root of unity. In this paper we prove that her formula, when replacing the third root of unity by an indeterminate $q$, is…
We initiate a systematic study of key-avoidance on alternating sign matrices (ASMs) defined via pattern-avoidance on an associated permutation called the \emph{key} of an ASM. We enumerate alternating sign matrices whose key avoids a given…
Linearized alternating direction method of multipliers (ADMM) as an extension of ADMM has been widely used to solve linearly constrained problems in signal processing, machine leaning, communications, and many other fields. Despite its…
The number of even 321-avoiding permutations of length n is equal to the number of odd ones if n is even, and exceeds it by the (n-1)/2th Catalan number otherwise. We present an involution that proves a refinement of this sign-balance…
When a matrix A with n columns is known to be well approximated by a linear combination of basis matrices B_1,..., B_p, we can apply A to a random vector and solve a linear system to recover this linear combination. The same technique can…
We study self-adjoint matrix polynomial equations in a single variable and prove existence of self-adjoint solutions under some assumptions on the leading form. Our main result is that any self-adjoint matrix polynomial equation of odd…
The nineteen-vertex model on a periodic lattice with an anti-diagonal twist is investigated. Its inhomogeneous transfer matrix is shown to have a simple eigenvalue, with the corresponding eigenstate displaying intriguing combinatorial…
In this article we provide with combinatorial proofs of some recent identities due to Sury and McLaughlin. We show that, the solution of a general linear recurrence with constant coefficients can be interpreted as a determinant of a matrix.…
Arc permutations, which were originally introduced in the study of triangulations and characters, have recently been shown to have interesting combinatorial properties. The first part of this paper continues their study by providing signed…
Much of modern Schubert calculus is centered on Schubert varieties in the complete flag variety and on their classes in its integral cohomology ring. Under the Borel isomorphism, these classes are represented by distinguished polynomials…
This paper investigates two issues on identification of switched linear systems: persistence of excitation and numerical algorithms. The main contribution is a much weaker condition on the regressor to be persistently exciting that…
Mixed linear regression involves the recovery of two (or more) unknown vectors from unlabeled linear measurements; that is, where each sample comes from exactly one of the vectors, but we do not know which one. It is a classic problem, and…