Planar kinematics: Cyclic fixed points, mirror superpotential, $k$-dimensional Catalan numbers, and root polytopes

• Published in: Annales de l'Institut Henri Poincaré. D. Combinatorics, physics and their interactions Vol. 12; no. 2; pp. 207 - 264
• Main Authors: Cachazo, Freddy, Early, Nick
• Format: Journal Article
• Language: English
• Published: 31.03.2025

In this paper, we prove that points in the space X(k,n) of configurations of n points in \mathbb{CP}^{k-1} which are fixed under a certain cyclic action are the solutions to the generalized scattering equations on planar kinematics (PK). In the first part, we give a constructive upper bound: we show...