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

<p>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].</p> <p>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 J&ouml;rg Rambau using the new <em>topcom</em> package described in [3].</p> <p>The provided data comes in three parts.</p> <ul> <li>The files ending in ".result" contain the original&nbsp;<em>topcom</em> output including the specific regular triangulations of the root polytope.</li> <li>There are <em>julia</em> files that contain these triangulations ("triangulations_x.jl"), one triangulation per line.</li> <li>There is an&nbsp;<em>OSCAR</em> script ("read_triangulations.jl") that reads these triangulations and produces sample metrics associated with each of these triangulations.&nbsp;</li> </ul> <h3>References:</h3> <p>[1] J. Gordon and F. Petrov: Combinatorics of the Lipschitz polytope, 2017, &nbsp;Arnold Math. J. <em>3.2.</em></p> <p>[2] E. Delucchi, L. K&uuml;hne, and L. M&uuml;hlherr: <em>Combinatorial invariants of finite metric spaces and the Wasserstein arrangement</em>, 2024, in preparation.</p> <p>[3] J. Rambau: <em>Symmetric lexicographic subset reverse search for the enumeration of circuits, cocircuits, and triangulations up to symmetry, </em>2023, <a href="https://www.wm.uni-bayreuth.de/de/team/rambau_joerg/TOPCOM/SymLexSubsetRS-2.pdf" target="_blank" rel="noopener">preprint</a>.</p>