A partial order structure on interval orders

TL;DR

This paper introduces a lattice structure on the set of interval orders, providing methods to compute meet and join, and connects it to the classical Tamari poset for series parallel interval orders.

Contribution

It defines a new partial order on interval orders, proves it forms a lattice, and relates it to the Tamari poset for series parallel cases.

Findings

The set of interval orders forms a lattice under the new partial order.

Methods for computing meet and join in this lattice are provided.

The classical Tamari poset is recovered for series parallel interval orders.

Abstract

We introduce a partial order structure on the set of interval orders of a given size, and prove that such a structure is in fact a lattice. We also provide a way to compute meet and join inside this lattice. Finally, we show that, if we restrict to series parallel interval order, what we obtain is the classical Tamari poset.