Roles of classic number triangles in computing scattering amplitudes

Question

Several classic number triangles--the Eulerian and Narayana numbers, in particular--appear in discussions of geometric structures, such as the amplituhedron, used in calculating the scattering amplitudes for certain physical theories. I wrote up a rough sketch of some of these relations in a blog post with numerous references--"An Intriguing Tapestry: Number triangles, polytopes, grassmannians, and scattering amplitudes" (https://tcjpn.wordpress.com/2016/11/20/an-intriguing-tapestry-number-triangles-polytopes-grassmannians-and-scattering-amplitudes/).

What are some other newer references that cast some light on the connections among these geometric structures, scattering amplitudes, and classic number arrays?