Related papers: A criterion for the half-plane property

We partition in classes the set of matroids of fixed dimension on a fixed vertex set. In each class we identify two special matroids, respectively with minimal and maximal h-vector in that class. Such extremal matroids also satisfy a…

We prove that r independent homogeneous polynomials of the same degree d become dependent when restricted to any hyperplane if and only if their inverse system parameterizes a variety whose (d-1)-osculating spaces have dimension smaller…

We compute the equation of the 7-secant variety to the Veronese variety (P^4,O(3)), its degree is 15. This is the last missing invariant in the Alexander-Hirschowitz classification. It gives the condition to express a homogeneous cubic…

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…

Given any polynomial with real coefficients, the existence of a real quadratic polynomial factor is proven using only basic real analysis. The aim is to provide an approachable proof to anybody who is familiar with the least upper bound…

This paper investigates a well-posedness property of parametric constraint systems named here Robinson stability. Based on advanced tools of variational analysis and generalized differentiation, we derive first-order and second-order…

In this note we aim to give a new, elementary proof of a statement that was first proved by Timofte. It says that a symmetric real polynomial $F$ of degree $d$ in $n$ variables is positive on $\R^n$ (on $\R^{n}_{\geq 0}$) if and only if it…

Let R be a commutative ring with 1. For every homogeneous polynomial f(X_0,X_1,X_2) in R[X_0,X_1,X_2] of degree d <= 25, we find a explicit linear Pfaffian R-representation of f. We describe an empirical method that leads us to find such…

A locally compact stable plane of positive topological dimension will be called semiaffine if for every line $L$ and every point $p$ not in $L$ there is at most one line passing through $p$ and disjoint from $L$. We show that then the plane…

When a monomial ideal has linear quotients with respect to an admissible order of increasing support-degree, we provide two proofs of different flavors to show that it is componentwise support-linear. We also introduce the variable…

In this note, we show that the algebraicity of the Fourier coefficients of half-integral weight modular forms can be determined by checking the algebraicity of the first few of them. We also give a necessary and sufficient condition for a…

We investigate structural properties of the cone of roots of relative Steiner polynomials of convex bodies. We prove that they are closed, monotonous with respect to the dimension, and that they cover the whole upper half-plane, except the…

We formulate a criterion for the existence of an invariant measure for a Feller semigroup defined on a metric space with the e-property for bounded continuous functions and use it to prove the asymptotic stability of a semigroup satisfying…

We call a multivariable polynomial an Agler denominator if it is the denominator of a rational inner function in the Schur-Agler class, an important subclass of the bounded analytic functions on the polydisk. We give a necessary and…

We describe a new subclass of the class of real polynomials with real simple roots called self-interlacing polynomials. This subclass is isomorphic to the class of real Hurwitz stable polynomials (all roots in the open left half-plane). In…

We provide a formula for the Ehrhart polynomial of the connected matroid of size $n$ and rank $k$ with the least number of bases, also known as a minimal matroid. We prove that their polytopes are Ehrhart positive and $h^*$-real-rooted (and…

In this survey we determine an explicit set of generators of the maximal ideals in the ring $\mathbb R[x_1,\dots,x_n]$ of polynomials in $n$ variables with real coefficients and give an easy analytic proof of the Bass-Vasershtein theorem on…

Questions concerning small fractional parts of polynomials and pseudo-polynomials have a long history in analytic number theory. In this paper, we improve on earlier work by Madritsch and Tichy. In particular, let $f=P+\phi$ where $P$ is a…

We establish a criterion for a complex number to be algebraic over Q of degree at most two. It requires that, for any sufficiently large real number X, there exists a non-zero polynomial with integral coefficients, of degree at most two and…

We consider multivariable polynomials over a fixed number field, linear in some of the variables. For a system of such polynomials satisfying certain technical conditions we prove the existence of search bounds for simultaneous zeros with…