Given a permutation sigma of the element of a finite field F_q, the permutation polynomial f_sigma in F_q[x] is the unique polynomial with degree less than q-1 that has the property that f_sigma(t)=sigma(t) for every t in F_q. We consider the natural question of enumerating the permutations in a given conjugacy class for which the permutation polynomial has degree less than q-2. we give formulas that ewxted existing ones. Furthermore for the case of k-cycles, we consider the harder problem of enumerating the permutations within a given conjugacy class for which the permutation polynomial has minimal degree. After giving an upper bound and a lower bound (for q congruent to 1 mod k) we consider various examples in which interesting Galois properties arise.

On the Enumeration of Permutation Polynomials / Malvenuto, Claudia; Pappalardi, Francesco. - STAMPA. - 20(2000), pp. 233-240. [E233232].

On the Enumeration of Permutation Polynomials

MALVENUTO, Claudia;
2000

Abstract

Given a permutation sigma of the element of a finite field F_q, the permutation polynomial f_sigma in F_q[x] is the unique polynomial with degree less than q-1 that has the property that f_sigma(t)=sigma(t) for every t in F_q. We consider the natural question of enumerating the permutations in a given conjugacy class for which the permutation polynomial has degree less than q-2. we give formulas that ewxted existing ones. Furthermore for the case of k-cycles, we consider the harder problem of enumerating the permutations within a given conjugacy class for which the permutation polynomial has minimal degree. After giving an upper bound and a lower bound (for q congruent to 1 mod k) we consider various examples in which interesting Galois properties arise.
2000
PUBLICATIONS DU LABORATOIRE DE COMBINATOIRE ET D'INFORMATIQUE MATHÉMATIQUE
2-89276-179-4
Permutation Polynomial
02 Pubblicazione su volume::02a Capitolo o Articolo
On the Enumeration of Permutation Polynomials / Malvenuto, Claudia; Pappalardi, Francesco. - STAMPA. - 20(2000), pp. 233-240. [E233232].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/802796
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