A characterization of barycentrically preassociative functions

TL;DR

This paper characterizes barycentrically preassociative functions as compositions of length-preserving associative string functions with injective unary maps, providing insights into their structure and implications.

Contribution

It offers a novel characterization of barycentrically preassociative functions through compositions involving associative string functions and injective unary maps.

Findings

Characterization of barycentrically preassociative functions

Connection between these functions and associative string functions

Discussion of implications and consequences of the characterization

Abstract

We provide a characterization of the variadic functions which are barycentrically preassociative as compositions of length-preserving associative string functions with one-to-one unary maps. We also discuss some consequences of this characterization.