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.