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

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Mar 2012Embargo end date: 01 Jan 2010 France, Luxembourg, Hungary English Publisher:Elsevier BVJournal:Discrete Applied Mathematics, volume 160, pages 383-390 (issn: 0166-218X,

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Authors: Miguel Couceiro; Erkko Lehtonen; Tamás Waldhauser;

doi: 10.1016/j.dam.2011.07.024 , 10.48550/arxiv.1003.2192

arXiv: 1003.2192

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

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Abstract

The aim of this paper is to classify order-preserving functions according to their arity gap. Noteworthy examples of order-preserving functions are 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.

11 pages, material reorganized

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France, Luxembourg, Hungary

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Keywords

Operations and polynomials in algebraic structures, primal algebras, Physique, chimie, mathématiques & sciences de la terre, 512, pseudo-Boolean function, order-preserving function, 510, Physical, chemical, mathematical & earth Sciences, FOS: Mathematics, Order-preserving function, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Boolean functions, aggregation function, 08A40, Applied Mathematics, Algèbre, Owen extension, Mathematics - Rings and Algebras, arity gap, 004, Mathématiques, Rings and Algebras (math.RA), Arity gap, Aggregation function, Boolean programming, Combinatorics (math.CO), Lovász extension, Mathematics

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