  The (tree) amplituhedron $\mathcal{A}_{n, k, m}$ is introduced by
Arkani-Hamed and Trnka in 2013 in the study of $\mathcal{N}=4$ supersymmetric
Yang-Mills theory. It is defined in terms of the totally nonnegative
Grassmannians. In this paper, we show that the amplituhedron $\mathcal{A}_{n,
k, m}$ for $m=2$ admits a triangulation. Our collection of cells is constructed
via BCFW-type recursion. We also provide a diagrammatic interpretation of our
construction.

Combinatorics;High Energy Physics - Theory;Representation Theory