Best values for the distributivity spectrum

TL;DR

This paper establishes optimal bounds for the distributivity spectrum in 4-distributive varieties, advancing the understanding of algebraic structures with specific distributive properties.

Contribution

It provides the first precise bounds for the distributivity spectrum in 4-distributive varieties and explores some partial generalizations.

Findings

Optimal bounds for $eta (eta ext{ composed with } eta)$ in 4-distributive varieties

Partial generalizations of the bounds to other cases

Enhanced understanding of distributive properties in algebraic structures

Abstract

We provide optimal bounds for $\alpha (\beta \circ \gamma \circ \dots )$ in $4$-distributive varieties, as well as some further partial generalizations.