Permuting 2-uniform tolerances on lattices

TL;DR

This paper characterizes when pairs of 2-uniform tolerances on finite-length lattices permute, showing that any two 2-uniform congruences on such lattices always permute, thereby advancing the understanding of lattice tolerances.

Contribution

It provides a complete characterization of permuting pairs of 2-uniform tolerances on finite-length lattices, highlighting that all such pairs of 2-uniform congruences permute.

Findings

Any two 2-uniform congruences on finite-length lattices permute

Characterization of permuting pairs of 2-uniform tolerances

Advances understanding of tolerance relations on lattices

Abstract

A $2$-uniform tolerance on a lattice is a compatible tolerance relation such that all of its blocks are 2-element. We characterize permuting pairs of 2-uniform tolerances on lattices of finite length. In particular, any two 2-uniform congruences on such a lattice permute.