On derivatives of planar mappings and their connections to complete mappings
Given are necessary conditions for a permutation polynomial to be the derivative of a planar mapping. These conditions are not sufficient and there might exist permutation polynomials which are not derivatives of some planar mapping satisfying these conditions. For the first time we show that there is a close connection between two seemingly unrelated structures, namely planar and complete mappings. It is shown that any planar mapping induces a sequence of complete mappings having some additional interesting properties. Furthermore, a class of almost planar mappings over extension fields is introduced having the property that its derivatives are permutations in most of the cases. This class of functions then induces many infinite classes of complete mappings (permutations) as well.
2018
2018-12-19 07:28:31
1033
planar mapping, derivatives, complete mappings, permutation polynomials
planarne funkcije, derivati, kompletne permutacije, permutacijski polinomi
Amela
Muratović-Ribić
70
Enes
Pašalić
70
UDK
4
51
ISSN pri članku
9
0166-218X
OceCobissID
13
25342464
COBISS_ID
3
1540927940
DOI
15
10.1016/j.dam.2018.04.023
0
Predstavitvena datoteka
2018-12-19 07:28:34