# Dickson Polynomials

### Some articles on dickson polynomials, polynomials, polynomial, dickson, dickson polynomial:

Dickson Polynomial
... In mathematics, the Dickson polynomials (or Brewer polynomials), denoted Dn(x,α), form a polynomial sequence introduced by L ... Dickson (1897) and rediscovered by Brewer (1961) in his study of Brewer sums ... Over the complex numbers, Dickson polynomials are essentially equivalent to Chebyshev polynomials with a change of variable, and in fact Dickson polynomials are sometimes called Chebyshev ...
Dickson Polynomial - Links To Other Polynomials
... Dickson polynomials over the complex numbers are related to Chebyshev polynomials Tn and Un by Crucially, the Dickson polynomial Dn(x,a) can be defined over rings in ... The Dickson polynomials with parameter α = 1 or α = -1 are related to the Fibonacci and Lucas polynomials ... The Dickson polynomials with parameter α = 0 give monomials ...
Permutation Polynomials and Dickson Polynomials
... A permutation polynomial (for a given finite field) is one that acts as a permutation of the elements of the finite field ... The Dickson polynomial Dn(x,α) (considered as a function of x with α fixed) is a permutation polynomial for the field with q elements whenever n is coprime to q2−1 ... Fried (1970) proved that any integral polynomial that is a permutation polynomial for infinitely many prime fields is a composition of Dickson polynomials and linear ...