Positroids, Plabic Graphs, and Scattering Amplitudes in Mathematica
Jacob L. Bourjaily
TL;DR
The paper introduces a public Mathematica package, 'positroids', designed to facilitate systematic exploration of the connections among on-shell diagrams, scattering amplitudes, and the positroid stratification of the Grassmannian $G(k,n)$. It provides tools to construct canonical coordinates for positroids, draw and analyze plabic graphs, and evaluate invariant on-shell differential forms, supplemented by a demonstration notebook and arXiv-provided source. Core capabilities include permutation-based boundary analysis, explicit BCFW-bridge coordinate expressions in terms of minors, and numerical kinematics via spinor or momentum-twistor data, enabling practical computation of on-shell functions and amplitudes. This toolkit lowers barriers to studying the positive Grassmannian in the context of planar $\mathcal{N}=4$ SYM and on-shell methods, offering a practical bridge between combinatorial geometry and scattering amplitudes.
Abstract
The many intricate connections between scattering amplitudes, on-shell diagrams, and the positroid stratification of the Grassmannian has recently been described in great detail. In order to facilitate the exploration of this rich correspondence, we have prepared a public Mathematica package called "positroids" which includes an array of useful tools including those for the construction of canonical coordinates for positroid configurations, the drawing of representative on-shell (plabic) graphs, and the evaluation of on-shell differential forms. This note documents the functions made available by the positroids package; the package's source code together with a Mathematica notebook containing many detailed examples of its functionality are included with this note's submission files on the arXiv.