TITLE: An Intriguing Tapestry: Number triangles, polytopes, Grassmannians, and scattering amplitudes
QUESTION [6 upvotes]: What are the roles that the classic number arrays-- Eulerian, Narayana--play in the application of totally non-negative Grassmannians, or amplituhedrons, to string / twistor scattering theory?
(This is a severely reduced version of the original post, which can be found at my blog https://tcjpn.wordpress.com/2016/11/20/an-intriguing-tapestry-number-triangles-polytopes-grassmannians-and-scattering-amplitudes/, with numerous references to the combinatorics of the associahedra and permutohedra and relations to scattering theory and Grassmannians.)

REPLY [4 votes]: In this recent preprint of Postnikov https://arxiv.org/abs/1806.05307 (which is for an upcoming ICM talk in Rio) he explains a beautiful direct connection between the geometry of the positive Grassmannian and the combinatorics of hypersimplices (polytopes whose normalized volume are the Eulerian numbers).