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.
planar mapping
derivatives
complete mappings
permutation polynomials
planarne funkcije
derivati
kompletne permutacije
permutacijski polinomi
true
true
false
Angleški jezik
Angleški jezik
Neznano
2018-12-19 07:28:31
2018-12-19 07:28:31
2018-12-20 03:01:27
2018
0
0
str. 285-290
#Vol. #250
Dec. 2018
0000-00-00
NiDoloceno
NiDoloceno
51
0166-218X
25342464
1540927940
10.1016/j.dam.2018.04.023
https://www.sciencedirect.com/science/article/pii/S0166218X18302439?via%3Dihub
https://repozitorij.upr.si/Dokument.php?lang=slv&id=15790
Inštitut Andrej Marušič