Reference : The arity gap of order-preserving functions and extensions of pseudo-Boolean functions
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/3162
The arity gap of order-preserving functions and extensions of pseudo-Boolean functions
English
Couceiro, Miguel mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Lehtonen, Erkko mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >]
Waldhauser, Tamás mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2012
Discrete Applied Mathematics
Elsevier
160
4-5
383-390
Yes (verified by ORBilu)
International
0166-218X
[en] arity gap ; order-preserving function ; aggregation function ; Owen extension ; Lovász extension
[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.
http://hdl.handle.net/10993/3162
10.1016/j.dam.2011.07.024

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