Eulerian partitions for configurations of skew lines

TL;DR

This paper explores elementary invariants of skew line configurations, introduces a natural partition of lines, and presents an algorithm to construct or disprove spindle-permutations for switching classes.

Contribution

It simplifies the exposition of known invariants and introduces an algorithm for constructing or disproving spindle-permutations in skew line configurations.

Findings

Defined a natural partition of lines in skew configurations

Developed an algorithm for constructing spindle-permutations

Provided methods to prove non-existence of spindle-permutations

Abstract

In this paper, which is a complement of \cite{BG}, we study a few elementary invariants for configurations of skew lines, as introduced and analyzed first by Viro and his collaborators. We slightly simplify the exposition of some known invariants and use them to define a natural partition of the lines in a skew configuration. We also describe an algorithm which constructs a spindle-permutation for a given switching class, or proves non-existence of such a spindle-permutation.