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

Miguel Couceiro (1) , Erkko Lehtonen (2) , Tamas Waldhauser (1)

1 Mathematics Research Unit
2 University of Luxembourg [Luxembourg]

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.

Domaines: Mathématiques [math]

Miguel Couceiro, Erkko Lehtonen, Tamas Waldhauser. The arity gap of order-preserving functions and extensions of pseudo-Boolean functions. Discrete Applied Mathematics, 2012, 160 (4-5), pp.383-390. ⟨10.1016/j.dam.2011.07.024⟩. ⟨hal-01090604⟩