Complete mappings and Carlitz rank

2016/04/26 by Işık, Leyla, Topuzoğlu, Alev, Winterhof, Arne
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.07710

Abstract

The well-known Chowla and Zassenhaus conjecture, proven by Cohen in 1990, states that for any d≥ 2 and any prime p>(d²-3d+4)² there is no complete mapping polynomial in \mathbbF_p[x] of degree d. For arbitrary finite fields \mathbbF_q, we give a similar result in terms of the Carlitz rank of a permutation polynomial rather than its degree. We prove that if n

Related

• On the difference between permutation polynomials over finite fields
• Permutation Polynomials with Carlitz Rank 2
• Permutation polynomials of finite fields
• The Weil bound and non-exceptional permutation polynomials over finite fields
• Ranges of polynomials control degree ranks of Green and Tao over finite prime fields