Parametrized arity gap

Couceiro, Miguel; Lehtonen, Erkko; Waldhauser, Tamás

doi:10.1007/s11083-012-9261-5

Reference : Parametrized arity gap


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/4463

Title :	Parametrized arity gap
Language :	English
Author, co-author :	Couceiro, Miguel [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
	Lehtonen, Erkko [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >]
	Waldhauser, Tamás [University of Szeged > Bolyai Institute]
Publication date :	2013
Journal title :	Order : A Journal on the Theory of Ordered Sets and its Applications
Publisher :	Springer
Volume :	30
Issue/season :	2
Pages :	557-572
Peer reviewed :	Yes
Audience :	International
ISSN :	0167-8094
e-ISSN :	1572-9273
City :	Dordrecht
Country :	Germany
Keywords :	[en] arity gap ; parametrized arity gap ; essential variable ; simple minor ; variable identification minor
Abstract :	[en] We propose a parametrized version of arity gap. The parametrized arity gap gap(f,l) of a function f: Aⁿ → B measures the minimum decrease in the number of essential variables of f when l consecutive identifications of pairs of essential variables are performed. We determine gap(f,l) for an arbitrary function f and a positive integer l. We also propose other variants of arity gap and discuss further problems pertaining to the effect of identification of variables on the number of essential variables of functions.
Permalink :	http://hdl.handle.net/10993/4463
DOI :	10.1007/s11083-012-9261-5
Mentions required by the publisher for OA :	The final publication is available at link.springer.com.

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