an:05004384
Zbl 1163.11350
Konyagin, Sergei; Pappalardi, Francesco
Enumerating permutation polynomials over finite fields by degree. II
EN
Finite Fields Appl. 12, No. 1, 26-37 (2006).
00122629
2006
j
11T06 05A16 11T23
Permutation polynomials; Finite fields; Exponential sums
Summary: This note is a continuation of Part I [Finite Fields Appl. 8, 548--553 (2002; Zbl 1029.11067)]. First we extend the method of the previous paper proving an asymptotic formula for the number of permutations for which the associated permutation polynomial has \(d\) coefficients in specified fixed positions equal to 0. This also applies to the function \(N_{q,d}\) that counts the number of permutations for which the associated permutation polynomial has degree \(< q-d-1\). Next we adopt a more precise approach to show that the asymptotic formula \(N_{q,d} \sim q!/q^d\) holds for \(d\leq\alpha q\) and \(\alpha=0.03983\).
Zbl 1029.11067