Related papers: On polynomials of binomial type, exponential integ…
In this paper we present and analyse a construction of irreducible polynomials over odd prime fields via the transforms which take any polynomial $f \in \mathbf{F}_p[x]$ of positive degree $n$ to $\left(\frac{x}{k} \right)^n \cdot…
We are concerned with polynomial involutions in characteristic two. In this note, we look for involutions among triangular automorphisms of the four-dimensional polynomial ring in characteristic two and obtain three types of such…
It is shown by the author in [J. Lie Theory 29:4, 1045-1070, 2019] that for every connected linear complex Lie group the algebra of polynomials (regular functions) is dense in the algebra of holomorphic functions of exponential type.…
In this paper, the compositional inverses of a class of linearized permutation polynomials of the form $P(x)=x+x^2+\tr(\frac{x}{a})$ over the finite field $\mathbb{F}_{2^n}$ for an odd positive integer $n$ are explicitly determined.
In this paper, we obtain a general expression for the entries of the lth (l is integer) powers of even order (2k+1)-diagonal Toeplitz matrices. Additionally, we have the complex factorizations of Fibonacci polynomials.
For any finite field $\mathbb{F}$ and any positive integer $n$ we count the number of monic polynomials of degree $n$ over $\mathbb{F}$ with nonzero constant coefficient and a self-reciprocal factor of any specified degree. An application…
In this paper, we consider the q-extensions of Boole polynomials. From those polynomials, we derive some new and interesting properties and identities related to special polynomials.
Supertropical matrix theory was investigated in [6], whose terminology we follow. In this work we investigate eigenvalues, characteristic polynomials and coefficients of characteristic polynomials of supertropical matrices and their powers,…
For a polynomial P, we consider the sequence of iterated integrals of ln P(x). This sequence is expressed in terms of the zeros of P(x). In the special case of ln(1 + x^2), arithmetic properties of certain coefficients arising are…
We study modular polynomials classifying cyclic isogenies between Drinfeld modules of arbitrary rank over the ring F_q[T].
We introduce the notion of numerical functors to generalise Eilenberg & MacLane's polynomial functors to modules over a binomial base ring. After shewing how these functors are encoded by modules over a certain ring, we record a precise…
There are two kinds of polynomial functions on matrix algebras over commutative rings: those induced by polynomials with coefficients in the algebra itself and those induced by polynomials with scalar coefficients. In the case of algebras…
Most integers are composite and most univariate polynomials over a finite field are reducible. The Prime Number Theorem and a classical result of Gau{\ss} count the remaining ones, approximately and exactly. For polynomials in two or more…
In some previous papers we have obtained characterizations (we called them characterizations of Lambek-Carlitz type) of some class of formal power series. Now, we discuss, investigate and compare these results from a categorial point of…
This paper is devoted to the study of the log-convexity of combinatorial sequences. We show that the log-convexity is preserved under componentwise sum, under binomial convolution, and by the linear transformations given by the matrices of…
A positive integer k is a length of a polynomial if that polynomial factors into a product of k irreducible polynomials. We find the set of lengths of polynomials of the form x^n in R[x], where (R, m) is an Artinian local ring with m^2 = 0.
Our paper deals about identities involving Bell polynomials. Some identities on Bell polynomials derived using generating function and successive derivatives of binomial type sequences. We give some relations between Bell polynomials and…
In this paper, we consider degenerate Carlitz's type q-Euler polynmials and numbers and we investigate some identities arising from the fermionic p-adic integral equations and the generating function of thoe polynomials.
We investigate fixed points and cycle types of permutation polynomials and complete permutation polynomials arising from reversed Dickson polynomials of the first kind and second kind over $\mathbb{F}_p$. We also study the permutation…
The use of permutation polynomials has appeared, along to their compositional inverses, as a good choice in the implementation of cryptographic systems. Hence, there has been a demand for constructions of these polynomials which…