Related papers: Exceptional scattered sequences
In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.
The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these…
Planar functions are special functions from a finite field to itself that give rise to finite projective planes and other combinatorial objects. We consider polynomials over a finite field $K$ that induce planar functions on infinitely many…
In this paper we consider a new normalization of matrices obtained by choosing distinct codewords at random from linear codes over finite fields and find that under some natural algebraic conditions of the codes their empirical spectral…
We begin by introducing an extension of the traditional abundancy index to imaginary quadratic rings with unique factorization. After showing that many of the properties of the traditional abundancy index continue to hold in our extended…
In this paper we introduce and investigate a one-parameter family of polynomials. They are semisymmetric, i.e. symmetric in the variables with odd and even index separately. In fact, the family forms a basis of the space of semisymmetric…
A method for generating irreducible polynomials of degree n over the finite field GF(2) is proposed. The irreducible polynomials are found by solving a system of equations that brings the information on the internal properties of the…
Compound distributions allow construction of a rich set of distributions. Typically they involve an intractable integral. Here we use a quadrature approximation to that integral to define the quadrature compound family. Special care is…
We construct two families of orthogonal polynomials associated with the universal central extensions of the superelliptic Lie algebras. These polynomials satisfy certain fourth order linear differential equations, and one of the families is…
New criteria are shown that certain combinations of finite unimodal polynomials are unimodal. %Given unimodal polynomials with explicit expressions and dependent recursion relations, we propose an approach to determine their modes. As…
Assume that $m,s\in\mathbb N$, $m>1$, while $f$ is a polynomial with integer coefficients, $\text{deg}~f>1$, $f^{(i)}$ is the $i$th iteration of the polynomial $f$, $\kappa_n$ has a discrete uniform distribution on the set $\{0,1,\ldots,m^n…
The main purpose of this article is to introduce some new binomial difference sequence spaces of fractional order ${\tilde{\alpha}} $ along with infinite matrices. Some topological properties of these spaces are considered along with the…
Divisibility sequences are defined by the property that their elements divide each other whenever their indices do. The divisibility sequences that also satisfy a linear recurrence, like the Fibonacci numbers, are generated by polynomials…
We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal subriemannian geodesics in stratified…
We prove a conjecture that classifies exceptional numbers. This conjecture arises in two different ways, from cryptography and from coding theory. An odd integer $t\geq 3$ is said to be exceptional if $f(x)=x^t$ is APN (Almost Perfect…
Lunardon and Polverino construct a translation plane starting from a scattered linear set of pseudoregulus type in $\mathrm{PG}(1,q^t)$. In this paper a similar construction of a translation plane $\mathcal A_f$ obtained from any scattered…
In this paper we study a family of scattered $\F_q$--linear sets of rank $tn$ of the projective space $PG(2n-1,q^t)$ ($n \geq 1$, $t\geq 3$), called of {\it pseudoregulus type}, generalizing results contained in [G. Marino, O. Polverino, R.…
We extend the algorithms of Robinson, Smyth, and McKee--Smyth to enumerate all real-rooted integer polynomials of a fixed degree, where the first few (at least three) leading coefficients are specified. Additionally, we introduce new linear…
Let $q\geqslant 2$ be a fixed prime power. We prove an asymptotic formula for counting the number of monic polynomials that are of degree $n$ and have exactly $k$ irreducible factors over the finite field $\mathbb{F}_q$. We also compare our…
In this paper, we study a Lienard system of the form dot{x}=y-F(x), dot{y}=-x, where F(x) is an odd polynomial. We introduce a method that gives a sequence of algebraic approximations to the equation of each limit cycle of the system. This…