Results 61 to 70 of about 57,503 (225)

A classification of permutation polynomials of degree $7$ over finite fields

, 2018
Up to linear transformations, we give a classification of all permutation polynomials of degree $7$ over $\mathbb{F}_{q}$ for any odd prime power $q$, with the help of the SageMath software.Comment: 13 ...
Fan, Xiang
core   +1 more source

Dynamic S-Box Design Using a Novel Square Polynomial Transformation and Permutation [PDF]

, 2021
Amjad Hussain Zahid, Hamza Rashid, Mian Muhammad Umar Shaban, Soban Ahmad, Ehtezaz Ahmed, Muhammad Tallal Amjad, Muhammad Azfar Tariq Baig, Muhammad Junaid Arshad, Muhammad Nadeem Tariq, M. Tariq, Muhammad Ayaz Zafar, Abdul Basit   +11 more
openalex   +1 more source

Constructing Separable Arnold Snakes of Morse Polynomials

, 2019
We give a new and constructive proof of the existence of a special class of univariate polynomials whose graphs have preassigned shapes. By definition, all the critical points of a Morse polynomial function are real and distinct and all its critical ...
Sorea, Miruna-Stefana
core   +1 more source

A simple model of trees for unicellular maps [PDF]

Discrete Mathematics & Theoretical Computer Science, 2012
We consider unicellular maps, or polygon gluings, of fixed genus. In FPSAC '09 the first author gave a recursive bijection transforming unicellular maps into trees, explaining the presence of Catalan numbers in counting formulas for these objects.
Guillaume Chapuy, Valentin Feray, Eric Fusy   +2 more
doaj   +1 more source

Probabilistic degenerate derangement polynomials

Mathematical and Computer Modelling of Dynamical Systems
In combinatorics, a derangement is a permutation of the elements of a set, such that no element appears in its original position. The number of derangements of an [Formula: see text]-element set is called the [Formula: see text]th derangement number ...
Taekyun Kim, Dae San Kim, Dmitry V. Dolgy   +2 more
doaj   +1 more source

CONSTRUCTING PERMUTATION POLYNOMIALS OVER FINITE FIELDS [PDF]

Bulletin of the Australian Mathematical Society, 2013
AbstractIn this paper, we construct several new permutation polynomials over finite fields. First, using the linearised polynomials, we construct the permutation polynomial of the form ${ \mathop{\sum }\nolimits}_{i= 1}^{k} ({L}_{i} (x)+ {\gamma }_{i} ){h}_{i} (B(x))$ over ${\mathbf{F} }_{{q}^{m} } $, where ${L}_{i} (x)$ and $B(x)$ are linearised ...
Qin, Xiaoer, Hong, Shaofang
openaire   +2 more sources

On the class of square Petrie matrices induced by cyclic permutations

International Journal of Mathematics and Mathematical Sciences, 2004
Let n≥2 be an integer and let P={1,2,…,n,n+1}. Let Zp denote the finite field {0,1,2,…,p−1}, where p≥2 is a prime. Then every map σ on P determines a real n×n Petrie matrix Aσ which is known to contain information on the dynamical properties such as ...
Bau-Sen Du
doaj   +1 more source

Permutation polynomials on matrices

Linear Algebra and its Applications, 1987
Let R be a finite field or a residue class ring of the integers, and let \(R_{n\times n}\) denote the ring of \(n\times n\) matrices over R. The paper presents families of polynomials over R, which induce, by substitution, permutations of \(R_{n\times n}\). Such polynomials are called permutation polynomials of \(R_{n\times n}\).
James, N.S., Lidl, R.
openaire   +2 more sources

Permutation-Invariant-Polynomial Neural-Network-based Δ-Machine Learn-ing Approach: A Case for the HO2 Self-reaction and its Dynamics Study [PDF]

, 2022
Yang Liu, Jun Li
openalex   +1 more source

Permutation and local permutation polynomials of maximum degree

Afrika Matematika
Abstract Let $$\mathbb {F}_q$$ F q be the finite field with q elements and $$\mathbb {F}_q[x_1,\ldots , x_n]$$
Jaime Gutierrez, Jorge Jiménez Urroz
openaire   +4 more sources