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, see [1]. These polytopes and their properties are described in detail in [2].

The catalog of KRW polytopes was computed using certain regular triangulations of the full root polytope, see Section 4 in [2]. These regular triangulations were enumerated up to symmetry by Jörg Rambau using the new topcom package described in [3].

The provided data comes in three parts.

• The files ending in ".result" contain the original topcom output including the specific regular triangulations of the root polytope.
• There are julia files that contain these triangulations ("triangulations_x.jl"), one triangulation per line.
• There is an OSCAR script ("read_triangulations.jl") that reads these triangulations and produces sample metrics associated with each of these triangulations. 

References:

[1] J. Gordon and F. Petrov: Combinatorics of the Lipschitz polytope, 2017,  Arnold Math. J. 3.2.

[2] E. Delucchi, L. Kühne, and L. Mühlherr: Combinatorial invariants of finite metric spaces and the Wasserstein arrangement, 2024, in preparation.

[3] J. Rambau: Symmetric lexicographic subset reverse search for the enumeration of circuits, cocircuits, and triangulations up to symmetry, 2023, preprint.