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The Exponential Formula allows one to enumerate any class of combinatorialobjects built by choosing a set of connected components and placing a structureon each connected component which depends only on its size. There are multiplevariants of this result, including Speicher's result for noncrossingpartitions, as well as analogues of the Exponential Formula for series-reducedplanar trees and forests. In this paper we use these formulae to givegenerating functions contracted Grassmannian trees and forests, certain graphswhose vertices are decorated with a helicity. Along the way we enumeratebipartite planar trees and forests, and we apply our results to enumeratevarious families of permutations: for example, bipartite planar trees are inbijection with separable permutations. Our generating function for Grassmannianforests can be interpreted as the rank generating function for the boundarystrata of the momentum amplituhedron, an object which encodes the tree-levelS-matrix of maximally supersymmetric Yang-Mills theory. This allows us toverify that the Euler characteristic of the momentum amplituhedron is 1.

Grass trees and forests: Enumeration of Grassmannian trees and forests, with applications to the momentum amplituhedron