Related papers: Positivity certificates for linear recurrences

This paper deals with the evaluation of trust in public-key infrastructures. Different trust models have been proposed to interconnect the various PKI components in order to propagate the trust between them. In this paper we provide a new…

With techniques borrowed from quantum information theory, we develop a method to systematically obtain operator inequalities and identities in several matrix variables. These take the form of trace polynomials: polynomial-like expressions…

We introduce a protocol addressing the conformance test problem, which consists in determining whether a process under test conforms to a reference one. We consider a process to be characterized by the set of end-product it produces, which…

Motivated by various problems in physics and applied mathematics, we look for constraints and properties of real Fourier-positive functions, i.e. with positive Fourier transforms. Properties of the "Dirac comb" distribution and of its…

We shall settle the completeness of some classical positive propositional calculi (positive propositional calculi in which the so-called Peirce's law holds) by resorting to a close adaptation of Kalmar's completeness proof procedure. First…

A recurrence relation is said to have the Laurent property if all of its iterates are Laurent polynomials in the initial values with integer coefficients. We consider a family of nonlinear recurrences with the Laurent property, which were…

This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…

Recurrence plots were introduced to help aid the detection of signals in complicated data series. This effort was furthered by the quantification of recurrence plot elements. We now demonstrate the utility of combining recurrence…

Let A be an nxn (entrywise) positive matrix and let f(t)=det(I-t A). We prove that there always exists a positive integer N such that 1-f(t)^{1/N} has positive coefficients.

For an arbitrary homogeneous linear recurrence sequence of order d with constant coefficients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coefficients of these recurrences are given…

In this paper, we propose a numerical method for verifying the positiveness of solutions to semilinear elliptic equations. We provide a sufficient condition for a solution to an elliptic equation to be positive in the domain of the…

We conjecture recurrence relations satisfied by the degrees of some linearizable lattice equations. This helps to prove linear growth of these equations. We then use these recurrences to search for lattice equations that have linear growth…

This paper investigates the connexion between the Kannan-Lipton Orbit Problem and the polynomial invariant generator algorithm PILA based on eigenvectors computation. Namely, we reduce the problem of generating linear and polynomial…

One of the main issues in proof certification is that different theorem provers, even when designed for the same logic, tend to use different proof formalisms and produce outputs in different formats. The project ProofCert promotes the…

Binary quadratic Diophantine equations are of interest from the viewpoint of computational complexity theory. They contain as special cases many examples of natural problems apparantly occupying intermediate stages in the P-NP hierarchy,…

One of equivalents of the Riemann hypothesis is Li's criterion that all Li coefficients are positive. We study recurrence relations of Li coefficients in this note.

An expression for the coefficients of a linear iterative equation in terms of the parameters of the source equation is given both for equations in standard form and for equations in reduced normal form. The operator generating an iterative…

We formulate and prove a general recurrence relation that applies to integrals involving orthogonal polynomials and similar functions. A special case are connection coefficients between two sets of orthonormal polynomials, another example…

Given positive numbers p_1 < p_2 < ... < p_n, and a real number r let L_r be the n by n matrix with its (i,j) entry equal to (p_i^r-p_j^r)/(p_i-p_j). A well-known theorem of C. Loewner says that L_r is positive definite when 0 < r < 1. In…

We introduce a family of norms on the $n \times n$ complex matrices. These norms arise from a probabilistic framework, and their construction and validation involve probability theory, partition combinatorics, and trace polynomials in…