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The arity gap of order-preserving functions and extensions of pseudo-Boolean functions |
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| Authors: | Miguel Couceiro Erkko Lehtonen Tamás Waldhauser |
| Affiliation: | 1. Mathematics Research Unit, University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, L–1359 Luxembourg, Luxembourg;2. Computer Science and Communications Research Unit, University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, L–1359 Luxembourg, Luxembourg;3. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H–6720 Szeged, Hungary |
| Abstract: | 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. |
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