𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Enumerating Permutation Polynomials I: Permutations with Non-Maximal Degree

✍ Scribed by Claudia Malvenuto; Francesco Pappalardi

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
154 KB
Volume
8
Category
Article
ISSN
1071-5797

No coin nor oath required. For personal study only.

✦ Synopsis

Let C be a conjugation class of permutations of a finite field F q . We consider the function N C ðqÞ defined as the number of permutations in C for which the associated permutation polynomial has degree 5q À 2. In 1969, Wells proved a formula for N ½3 ðqÞ where ½k denotes the conjugation class of k-cycles. We will prove formulas for N ½k ðqÞ where k ¼ 4; 5; 6 and for the classes of permutations of type ½2 2; ½3 2; ½4 2; ½3 3 and ½2 2 2. Finally in the case q ¼ 2 n , we will prove a formula for the classes of permutations which are product of 2-cycles.

📜 SIMILAR VOLUMES

Enumerating Permutation Polynomials over
Enumerating Permutation Polynomials over Finite Fields by Degree
✍ Sergei Konyagin; Francesco Pappalardi 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 85 KB

We prove an asymptotic formula for the number of permutations for which the associated permutation polynomial has degree smaller than q À 2. # 2002 Elsevier Science (USA)

Transitive Permutation Groups with Bound
Transitive Permutation Groups with Bounded Movement Having Maximal Degree
✍ Akbar Hassani; Mehdi Khayaty; E.I Khukhro; Cheryl E Praeger 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 156 KB

Let G be a transitive permutation group on a set ⍀ such that G is not a 2-group and let m be a positive integer. It was shown by the fourth author that if < g < < < ? Ž . @ ⌫ \_ ⌫ F m for every subset ⌫ of ⍀ and all g g G, then ⍀ F 2 mpr p y 1 , < < < < where p is the least odd prime dividing G . If