The lists of 129 and 2328 copious graphs for $n=7$ and $8$ respectively, as well as the data with ML degrees, multidegrees and degrees of logarithmic discriminants (for graphs with a universal vertex) up to $n=8$ vertices are available in the following files: Data456.pdf Data7.pdf Data8.pdf The multidegrees for all 129 and 2328 copious graphs for $n=7$ and $8$ are contained in the following files: Multidegrees7.pdf Multidegrees8.pdf The corresponding csv versions of all these tables are available in the attachments. Most of our functions are written in $\texttt{Julia}$ and collected in the package ScatteringGraphs.zip.A Jupyter Notebook with examples of its usage is provided in ScatteringGraphsTutorial.ipynb.

This page contains auxiliary material for the paper Graphical Scattering Equations by Barbara Betti, Viktoriia Borovik, Bella Finkel, Bernd Sturmfels, and Bailee Zacovic. The CHY scattering equations on the moduli space $\mathcal{M}_{0,n}$ play a prominent role at the interface of particle physics and algebraic statistics. We study the scattering correspondence when the Mandelstam invariants are restricted to a fixed graph on $n$ vertices.

A detailed explanation how to convert a graph with a universal vertex to appropriate gauge fixing to compute the degree of the logarithmic discriminant is available in the Jupyter Notebook in the folder Discriminants.zip. There, it is done for all copious graphs with a universal vertex for $n=8$.A Macaulay2 code verifying Proposition 4.11 is available in the M2.zip folder.

A computer-aided proof of the Corollary 8.6 by Manuel Kauers is available at ProofOfCorollary8_6.pdf