Related papers: Local Method for Compositional Inverses of Permuta…
Permutation polynomials over finite fields are an interesting and constantly active research subject of study for many years. They have important applications in areas of mathematics and engineering. In recent years, permutation binomials…
We present an algorithm to find invariant poynomial transformations of integer sequences, using the classical invariant theory approach.
We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to…
In this paper, we study existence of solutions to a conformally invariant integral equation involving Poisson-type kernels. Such integral equation has a stronger non-local feature and is not the dual of any PDE. We obtain the existence of…
Spingarn's method of partial inverses has found many applications in nonlinear analysis and in optimization. We show that it can be employed to solve composite monotone inclusions in duality, thus opening a new range of applications for the…
In this paper, we present a linear algebraic approach to the study of permutation polynomials that arise from linear maps over a finite field $\mathbb{F}_{q^2}$. We study a particular class of permutation polynomials over…
A new method of composition orthogonality is introduced. It is applied to generate new sequences of orthogonal polynomials and functions. In particular, classical orthogonal polynomials are interpreted in the sense of composition…
The powers of generating functions and its properties are analyzed. A new class of functions is introduced, based on the application of compositions of an integer $n$, called composita. The methods for obtaining reciprocal and reverse…
In this paper, we present three classes of complete permutation monomials over finite fields of odd characteristic. Meanwhile, the compositional inverses of these complete permutation polynomials are also proposed.
The Compositional Integral is defined, formally constructed, and discussed. A direct generalization of Riemann's construction of the integral; it is intended as an alternative way of looking at First Order Differential Equations. This brief…
In this note, we give a shorter proof of the result of Zheng, Yu, and Pei on the explicit formula of inverses of generalized cyclotomic permutation polynomials over finite fields. Moreover, we characterize all these cyclotomic permutation…
We obtain explicit upper bounds for the number of irreducible factors for a class of compositions of polynomials in several variables over a given field. In particular, some irreducibility criteria are given for this class of compositions…
Recently, Jiang et al. \cite{JIANG2025102522} obtained several classes of Permutation Polynomial of the form $x+\gamma\operatorname{Tr}_q^{q^2}(h(x))$ over finite fields $\mathbb{F}_{q^2},q=2^n$. In this paper, we find the compositional…
We use a probabilistic method to produce some combinatorial inequalities by considering pattern containment in permutations and words.
Let $q$ be a prime power and $n$ and $r$ be positive integers. It is well known that the linearized binomial $L_r(x)=x^{q^r}+ax\in\mathbb{F}_{q^n}[x]$ is a permutation polynomial if and only if $(-1)^{n/d}a^{{(q^n-1)}/{(q^{d}-1)}}\neq 1$…
The aim of the present paper is to make some notes to the newly introduced conformable derivative as a type local fractional derivative and to present a surprising result about the relation between the conformable derivatives and the usual…
We introduce a new type of reduction of inversive difference polynomials that is associated with a partition of the basic set of automorphisms $\sigma$ and uses a generalization of the concept of effective order of a difference polynomial.…
In this paper, we study how to quickly compute the <-minimal monomial interpolating basis for a multivariate polynomial interpolation problem. We address the notion of "reverse" reduced basis of linearly independent polynomials and design…
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…
This paper introduces two forms of modular inverses and proves their reciprocity formulas respectively. These formulas are then applied to formulate new and generalized algorithm for computing these modular inverses. The same algorithm is…