Dimension bounds on classes of interval orders with restricted representation

TL;DR

This paper investigates the dimension of subclasses of interval orders with restricted interval lengths, answering open questions and providing simplified proofs for key results in this area.

Contribution

It introduces bounds on the dimension of interval order subclasses with restricted lengths and clarifies previous results with simplified proofs.

Findings

Answered several open questions about dimension bounds.

Provided simplified proofs for existing main results.

Established new bounds for classes with restricted interval lengths.

Abstract

In general, representations of interval orders may use an arbitrary set of interval lengths. We can define subclasses of interval orders by restricting the allowable lengths of intervals. Motivated by a recent paper of Keller, Trenk, and Young, we study the dimension of posets in some of these subclasses. Among other results, we answer several of their questions, and we simplify the proof of one of their main results.