Related papers: B\'ezout Subresultants for Univariate Polynomials …

We associate a polynomial to any diagram of unit cells in the first quadrant of the plane using Kohnert's algorithm for moving cells down. In this way, for every weak composition one can choose a cell diagram with corresponding row-counts,…

Polynomial regression is a recurrent problem with a large number of applications. In computer vision it often appears in motion analysis. Whatever the application, standard methods for regression of polynomial models tend to deliver biased…

A new global basis of B-splines is defined in the space of generalized quadratic splines (GQS) generated by Merrien subdivision algorithm. Then, refinement equations for these B-splines and the associated corner-cutting algorithm are given.…

We review the definition and main properties of differential subresultants in order to achieve their implementation in Maple, using the DEtools package. The focus is on computing GCRDs of ordinary differential operators with non necessarily…

Schubert polynomials form a basis of the polynomial ring. This basis and its structure constants have received extensive study. Recently, Pan and Yu initiated the study of top Lascoux polynomials. These polynomials form a basis of a…

Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations (Efron, 2013, Science). While it has…

We investigate in this paper a generalization of Solomon-Terao formula for central equidimensional subspace arrangements. We introduce generalized Solomon-Terao functions based on the Hilbert-Poincar\'e series of the modules of…

In this article, we prove some factorization results for several classes of polynomials having integer coefficients, which in particular yield several classes of irreducible polynomials. Such classes of polynomials are devised by imposing…

We give necessary and sufficient conditions for majorization of realrooted polynomials sharing a common interlacer by means of residues coming from fraction decomposition. We also introduce a motivated notion called strong majorization, and…

We have developed a patch implementing multivariate polynomials seen as a multi-base algebra. The patch is to be released into the software Sage and can already be found within the Sage-Combinat distribution. One can use our patch to define…

This paper is a study of power series, where the coefficients are binomial expressions (iterated finite differences). Our results can be used for series summation, for series transformation, or for asymptotic expansions involving Stirling…

In this paper, we provide a general framework for obtaining the formula for nested summation of powers of natural numbers. We define a special triangular array of numbers from which we can obtain the formula for nested summation of natural…

What polynomial in the coefficients of a system of algebraic equations should be called its discriminant? We prove a package of facts that provide a possible answer. Let us call a system typical, if the homeomorphic type of its set of…

We present new results and an algorithm for standard basis computations of a 0-dimensional ideal I in a power series ring or in the localization of a polynomial ring in finitely many variables over a field K. The algorithm provides a…

We introduce poly-Bernoulli polynomials in two variables by using a generalization of Stirling numbers of the second kind that we studied in a previous work. We prove the bi-variate poly-Bernoulli polynomial version of some known results on…

In this work, considering a general subclass of bi-univalent functions and using the Chebyshev polynomials, we obtain coefficient expansions for functions in this class.

The author in [7] was proved the generalized remainder and quotient theorems of polynomial in one indeterminate where the divisor is complete factorization to linear factors. In this paper we give the formula for the generalized remainder…

In this note we show a simple formula for the coefficients of the polynomial associated with the sums of powers of the terms of an arbitrary arithmetic progression. This formula consists of a double sum involving only ordinary binomial…

Let X be a finite set of points in R^n. A polynomial p nonnegative on X can be written as a sum of squares of rational functions modulo the vanishing ideal I(X). From the point of view of applications, such as polynomial optimization, we…

In this paper our aim is to present some subordination and superordination results, by using an operator, which involves the normalized form of the generalized Bessel functions of first kind. These results are obtained by investigating some…