On the number of simple arrangements of five double pseudolines

TL;DR

This paper introduces an incremental algorithm for enumerating isomorphism classes of double pseudoline arrangements, proving their connectedness under mutations and providing new counting results.

Contribution

It presents a novel incremental algorithm for enumeration and proves the connectedness of arrangement spaces, with new counting data included.

Findings

Algorithm successfully enumerates arrangements

Connectedness under mutations established

Counting results for arrangements reported

Abstract

We describe an incremental algorithm to enumerate the isomorphism classes of double pseudoline arrangements. The correction of our algorithm is based on the connectedness under mutations of the spaces of one-extensions of double pseudoline arrangements, proved in this paper. Counting results derived from an implementation of our algorithm are also reported.