Almost associative operations generating a minimal clone

TL;DR

This paper characterizes 'almost associative' binary operations that generate minimal clones, exploring two interpretations based on the associative spectrum and the index of nonassociativity, to understand their structural properties.

Contribution

It provides new characterizations of almost associative operations generating minimal clones using two different measures of nonassociativity.

Findings

Characterizations based on associative spectrum

Characterizations based on index of nonassociativity

Insights into the structure of minimal clones

Abstract

Characterizations of "almost associative" binary operations generating a minimal clone are given for two interpretations of the term "almost associative". One of them uses the associative spectrum, the other one uses the index of nonassociativity to measure how far an operation is from being associative.