Generating Posets with Interfaces

TL;DR

This paper introduces a new class of iposets with full interfaces, enabling enumeration and analysis of isomorphism classes of posets with interfaces, supported by Julia software and a polynomial-time isomorphism invariant.

Contribution

It defines a new class of iposets with full interfaces and demonstrates their sufficiency for enumeration, along with developing software and a polynomial-time isomorphism invariant.

Findings

Successfully generated and counted iposets up to eight points

Developed Julia software for poset exploration

Created a polynomial-time isomorphism invariant

Abstract

We generate and count isomorphism classes of gluing-parallel posets with interfaces (iposets) on up to eight points, and on up to ten points with interfaces removed. In order to do so, we introduce a new class of iposets with full interfaces and show that considering these is sufficient. We also describe the software (written in Julia) that we have used for our exploration and define a new incomplete isomorphism invariant which may be computed in polynomial time yet identifies only very few pairs of non-isomorphic iposets.