Dataset of Kantorovich-Rubinstein-Wasserstein Polytopes of Metric Spaces on up to 6 Points

We present a complete list of all combinatorial types of generic Kantorovich-Rubinstein-Wasserstein (KRW) polytopes associated with metric spaces on up to 6 points that are generic in the sense of Gordon and Petrov. These polytopes and their properties are described in detail in the preprint "Combinatorial invariants of finite metric spaces and the Wasserstein arrangement".

The catalog of KRW polytopes was computed using certain regular triangulations of the full root polytope. These regular triangulations were enumerated up to symmetry by Jörg Rambau using the new topcom package.

The provided data consists of:

• The files ending in ".result" contain the original topcom output including the specific regular triangulations of the root polytope.
•  julia files that contain these triangulations ("triangulations_x.jl"), one triangulation per line.
• An OSCAR script ("read_triangulations.jl") that reads these triangulations and produces sample metrics associated with each of these triangulations.
• A Jupyter notebook ("wasserstein_arrangement_code.ipynb") with OSCAR code to compute KRW polytopes as well as code to determine the representatives for the combinatorial types. For convenience, we also included the notebook as a julia script as well as a pdf of the notebook. 
• JSON files saved as .mrdi containing the collection of all KRW polytopes of strict and generic metrics for $n=5$ and all generic metrics for $n=6$ together with their corresponding metrics (one per combinatorial type). These files can be loaded in OSCAR via 

  load("Polytopes_generic_metrics_5.mrdi")

We used julia Version 1.12.6 with these packages:

• OSCAR v1.7.2
• CountingChambers v0.2.3
• Graphs v1.14.0