Related papers: A note concerning the invertibility of certain alt…

We present a more general proof that cyclotomic polynomials are irreducible over Q and other number fields that meet certain conditions. The proof provides a new perspective that ties together well-known results, as well as some new…

In this note we present a characterisation of all unary and binary patterns that do not only contain variables, but also reversals of their instances. These types of variables were studied recently in either more general or particular…

We are interested in matrices of minors of order p of a invertible matrix. Special cases are studied when this matrix is in SL(n) or SO(n)

Admissable weight is an important tool for studying spectral invariance in operator algebra. Common admissable weights include polynomial weights and sub exponential weights. This article mainly provides a proof that polynomial weights are…

In this paper, we obtain several new factorization results for certain classes of polynomials having integer coefficients. In doing so, we use the information about prime factorization of the value taken up by such polynomials and their…

Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.

We show that (as conjectured by Lin and Wang) when a Vassiliev invariant of type $m$ is evaluated on a knot projection having $n$ crossings, the result is bounded by a constant times $n^m$. Thus the well known analogy between Vassiliev…

This short note, in part of expository nature, points out several new or recent consequences of a quite nice decomposition for positive semi-definite matrices.

A practical criterion for the irreducibility (with respect to integration by part identities) of a particular Feynman integral to a given set of integrals is presented. The irreducibility is shown to be related to the existence of stable…

An elementary proof of the two-sidedness of the matrix-inverse is given using only linear independence and the reduced row-echelon form of a matrix. In addition, it is shown that a matrix is invertible if and only if it is row-equivalent to…

In these notes we focus a bit on the complex case for some families of matrices and equivalences between them.

We give a lower bound for the degree of an irreducible factor of a given polynomial. This improves and generalizes the results obtained in [4, On the irreducible factors of a polynomial, Proc. Amer. Math. Soc., 148 (2020] 1429 -- 1437].

Many questions in number theory concern the nonvanishing of determinants of square matrices of logarithms (complex or p-adic) of algebraic numbers. We present a new conjecture that states that if such a matrix has vanishing determinant,…

We prove that a random bivariate polynomial with plus minus 1 coefficients is irreducible with high probability.

In this paper, by using the theory of circulant matrices we study some matrices over finite fields which involve the quadratic character and trinomial coefficients.

We shall characterize the structure of invertible substitutions on three-letter alphabet. We show that any invertible substitution, after some cyclic operation, can be written as a finite product of permutations and Fibonacci's…

We describe isomorphisms of groups of several periodic infinite matrices and isomorphisms of groups of invertible elements of unital locally matrix algebras.

We prove that arithmetic is interpretable in any indecomposable polynomial ring (in any set of variables), and in addition we provide an alternative uniform proof of undecidability for all members in this class of rings.

We present here necessary and sufficient conditions for the invertibility of circulant and symmetric matrices that depend on three parameters and moreover, we explicitly compute the inverse. The techniques we use are related with the…

This work is divided into three parts. The first part concerns polynomials in one variable with all real roots. We consider linear transformations that preserve real rootedness, as well as matrices that preserve interlacing. The second part…