Relaxations of associativity and preassociativity for variadic functions
Group Theory
2016-06-21 v1 Discrete Mathematics
Rings and Algebras
Abstract
In this paper we consider two properties of variadic functions, namely associativity and preassociativity, that are pertaining to several data and language processing tasks. We propose parameterized relaxations of these properties and provide their descriptions in terms of factorization results. We also give an example where these parameterized notions give rise to natural hierarchies of functions and indicate their potential use in measuring the degrees of associativeness and preassociativeness. We illustrate these results by several examples and constructions and discuss some open problems that lead to further directions of research.
Keywords
Cite
@article{arxiv.1508.03310,
title = {Relaxations of associativity and preassociativity for variadic functions},
author = {Miguel Couceiro and Jean-Luc Marichal and Bruno Teheux},
journal= {arXiv preprint arXiv:1508.03310},
year = {2016}
}