Distinct orders dividing each other on both sides

TL;DR

This paper constructs examples of non-isomorphic linear orders that divide each other from both sides, answering a longstanding question in order theory.

Contribution

It provides the first explicit construction of such orders, demonstrating the existence of non-isomorphic mutual divisors.

Findings

Existence of non-isomorphic linear orders dividing each other

Positive answer to Sierpinski's question

Advancement in understanding order divisibility

Abstract

We construct non-isomorphic linear orders X and Y that are both left-hand and right-hand divisors of one another, answering positively a question of Sierpinski.