The arity gap of order-preserving functions and extensions of pseudo-Boolean functions
Rings and Algebras
2016-11-22 v3 Combinatorics
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 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.
Keywords
Cite
@article{arxiv.1003.2192,
title = {The arity gap of order-preserving functions and extensions of pseudo-Boolean functions},
author = {Miguel Couceiro and Erkko Lehtonen and Tamás Waldhauser},
journal= {arXiv preprint arXiv:1003.2192},
year = {2016}
}
Comments
11 pages, material reorganized