Reference : The arity gap of order-preserving functions and extensions of pseudo-Boolean functions

	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/3162

Title :	The arity gap of order-preserving functions and extensions of pseudo-Boolean functions
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 Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Publication date :	2012
Journal title :	Discrete Applied Mathematics
Publisher :	Elsevier
Volume :	160
Issue/season :	4-5
Pages :	383-390
Peer reviewed :	Yes (verified by ORBilu)
Audience :	International
ISSN :	0166-218X
Keywords :	[en] arity gap ; order-preserving function ; aggregation function ; Owen extension ; Lovász extension
Abstract :	[en] The aim of this paper is to classify order-preserving functions according to their arity gap. Noteworthy examples of order-preserving functions are the so-called aggregation functions. We first explicitly classify the Lovász extensions of pseudo-Boolean functions according to their arity gap. Then we consider the class of order-preserving functions between partially ordered sets, and establish a similar explicit classification for this function class.
Permalink :	http://hdl.handle.net/10993/3162
DOI :	10.1016/j.dam.2011.07.024

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