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.
Categories: math.CO hep-th math.RT