Related papers: Chandrasekhar polynomials -- A brief review
In this paper are characterized the polynomials, in terms of their coefficients, that have all their orbits dense in the set of 3-adic integers.
In this paper, we investigate some properties of several Sheffer sequences of several polynomials arising from umbral calculus. From our investigation, we can derive many interesting identities of several polynomials
We report on various results, conjectures, and open problems related to Kazhdan-Lusztig polynomials of matroids. We focus on conjectures about the roots of these polynomials, all of which appear here for the first time.
Orthogonal polynomials of two real variables can often be represented in complex variables. We explore the connection between the two types of representations and study the structural relations of complex orthogonal polynomials. The complex…
We introduce three kinds of invariants of a virtual knot called the first, second, and third intersection polynomials. The definition is based on the intersection number of a pair of curves on a closed surface. The calculations of…
We present a theorem about irreducibility of a polynomial that is the resultant of two others polynomials. The proof of this fact is based on the field theory. We also consider the converse theorem and some examples.
We prove certain identities involving Euler and Bernoulli polynomials that can be treated as recurrences. We use these and also other known identities to indicate connection of Euler and Bernoulli numbers with entries of inverses of certain…
We introduce a general framework for the construction of polynomial frames in $L^2(\mathbb{S}^{d-1})$, $d \geq 3$, where the frame functions are obtained as rotated versions of an initial sequence of polynomials $\Psi^j$, $j\in…
We investigate polynomials, called m-polynomials, whose generator polynomial has coefficients that can be arranged as a matrix, where q is a positive integer greater than one. Orthogonality relations are established and coefficients are…
In this paper we consider the notions of binomial thinning, binomial mixing, their generalizations, certain interplay between them, associated limit theorems and provide various examples.
Recursion formulae are derived for the calculation of two centre matrix elements of a radial function in relativistic quantum mechanics. The recursions are obtained between not necessarily diagonal radial eigensates using arbitrary radial…
We consider Tuenter polynomials as linear combinations of descending factorials and show that coefficients of these linear combinations are expressed via a Catalan triangle of numbers. We also describe a triangle of coefficients in terms of…
Permutation polynomials have been a subject of study for a long time and have applications in many areas of science and engineering. However, only a small number of specific classes of permutation polynomials are described in the literature…
The purpose of this review paper is the collection, systematization and discussion of recent results concerning the quantization approach to the Jacobian conjecture, as well as certain related topics.
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…
This paper is devoted to characterizations classical orthogonal polynomials on quadratic lattices by using a matrix approach. In this form we recover the Hahn, Geronimus, Tricomi and Bochner type characterizations of classical orthogonal…
Polynomial, C-finite, Holonomic are the most common ansatz to describe the pattern of the sequences. We propose a new ansatz called X-recursive that generalize those we mentioned. We also discuss its closure properties and compare this…
This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fields of science, the mathematics of the underlying model of…
Closely following recent ideas of J. Borcea, we discuss various modifications and relaxations of Sendov's conjecture about the location of critical points of a polynomial with complex coefficients. The resulting open problems are formulated…
We give formulas for the number of polynomials over a finite field with given root multiplicities, in particular in cases when the formula is surprisingly simple (a power of q). Besides this concrete interpretation, we also prove an…