On derivatives of planar mappings and their connections to complete mappings

Muratović-Ribić, Amela; Pašalić, Enes

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Title:	On derivatives of planar mappings and their connections to complete mappings
Authors:	ID Muratović-Ribić, Amela (Author) ID Pašalić, Enes (Author)
Files:	https://www.sciencedirect.com/science/article/pii/S0166218X18302439?via%3Dihub
Language:	English
Work type:	Unknown
Typology:	1.01 - Original Scientific Article
Organization:	IAM - Andrej Marušič Institute
Abstract:	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.
Keywords:	planar mapping, derivatives, complete mappings, permutation polynomials
Year of publishing:	2018
Number of pages:	str. 285-290
Numbering:	#Vol. #250
PID:	20.500.12556/RUP-10031
UDC:	51
ISSN on article:	0166-218X
DOI:	10.1016/j.dam.2018.04.023
COBISS.SI-ID:	1540927940
Publication date in RUP:	18.12.2018
Views:	2811
Downloads:	245
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Record is a part of a journal

Title:	Discrete applied mathematics
Shortened title:	Discrete appl. math.
Publisher:	Elsevier
ISSN:	0166-218X
COBISS.SI-ID:	25342464

Secondary language

Language:	English
Keywords:	planarne funkcije, derivati, kompletne permutacije, permutacijski polinomi

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