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

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

2010-03-10

arxiv.org/abs/1003.2192v3

Mathematics

Rings and Algebras

11 pages, material reorganized

Scientific paper

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 Lov\'asz 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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