Related papers: A Classification of Permutation Polynomials throug…

A permutation polytope is the convex hull of a group of permutation matrices. In this paper we investigate the combinatorics of permutation polytopes and their faces. As applications we completely classify permutation polytopes in…

Matrix polynomials given in an orthogonal basis are considered. Following the ideas of Mackey et al. "Vector spaces of Linearizations for Matrix Polynomials" (2006), the vec- tor spaces, called M1(P), M2(P) and DM(P), of potential…

Differential systems with a Fuchsian linear part are studied in regions including all the singularities in the complex plane of these equations. Such systems are not necessarily analytically equivalent to their linear part (they are not…

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…

We consider the logarithm of the characteristic polynomial of random permutation matrices, evaluated on a finite set of different points. The permutations are chosen with respect to the Ewens distribution on the symmetric group. We show…

Let $r\geq 3$ be any positive integer which is relatively prime to $p$ and $q^2\equiv 1 \pmod r$. Let $\tau_1, \tau_2$ be any permutation polynomials over $\mathbb{F}_{q^2},$ $\sigma_M$ is an invertible linear map over $\mathbb{F}_{q^2}$…

In this paper the main results in arXiv:0901.3179v3, related to the matrix representation of polynomial maps, are restated in traditional way of linear algebra assuming that variable vectors are presented as column vectors. Some new results…

We explore the connection between cyclotomic mapping permutation polynomials and permutation polynomials of the form $x^rf(x^{\frac{q-1}{l}})$ over finite fields. We present a new necessary and a new sufficient condition to verify…

Every Latin square of prime power order $q$ is uniquely described by a local permutation polynomial (LPP) in the polynomial ring $\mathbb{F}_q[x,y]$. Despite this equivalence, one may find in the literature only some preliminary results on…

If f is a polynomial with integer coefficients and q is an integer, we may regard f as a map from Z/qZ to Z/qZ. We show that the distribution of the (normalized) spacings between consecutive elements in the image of these maps becomes…

The main purpose of this paper is solve polynomial equations that are satisfied by (generalized) polynomials. More exactly, we deal with the following problem: let $\mathbb{F}$ be a field with $\mathrm{char}(\mathbb{F})=0$ and $P\in…

We present new classes of permutation polynomials over finite fields.

In \cite{D1}, Dickson listed all permutation polynomials up to degree 5 over an arbitrary finite field, and all permutation polynomials of degree 6 over finite fields of odd characteristic. The classification of degree 6 permutation…

Permutation polynomials with coefficients 1 over finite fields attract researchers' interests due to their simple algebraic form. In this paper, we first construct four classes of fractional permutation polynomials over the cyclic subgroup…

We study degree preserving maps over the set of irreducible polynomials over a finite field. In particular, we show that every permutation of the set of irreducible polynomials of degree $k$ over $\mathbb{F}_q$ is induced by an action from…

Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. In this paper, two conjectures on permutation polynomials proposed recently by Wu and Li [19] are…

Some polynomials $P$ with rational coefficients give rise to well defined maps between cyclic groups, $\Z_q\longrightarrow\Z_r$, $x+q\Z\longmapsto P(x)+r\Z$. More generally, there are polynomials in several variables with tuples of rational…

It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…

Let $q=4$ and $k$ a positive integer. In this short note, we present a class of permutation polynomials over $\Bbb F_{q^{3k}}$. We also present a generalization.

This paper came to existence out of the desire to understand iterations of strictly triangular polynomial maps over finite fields. This resulted in two connected results: First, we give a generalization of $\F_p$-actions on $\F_p^n$ and…