Collection of Polynomials over Finite Fields Providing Involutary Permutations

2023/06/28 by Vanchinathan, P, B, Kevinsam
#11T06 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2306.16038

Abstract

For an odd prime power q satisfying q≡ 1\pmod 3 we construct totally 2(q-1) permutation polyomials, all giving involutory permutations with exactly 1+ \fracq-13 fixed points. Among them (q-1) polynomials are trinomials, and the rest are 6-term polynomials.

Related

• Involutary pemutations over finite fields given by trinomials and quadrinomials
• A note on permutation polynomials over finite fields
• Construction of Permutation Polynomials of Certain Specific Cycle Structure over Finite Fields
• A Class of Permutation Binomials over Finite Fields
• Permutation polynomials over finite fields from low-degree rational functions