The m=2 amplituhedron and the hypersimplex: signs, clusters, triangulations, Eulerian numbers

Matteo Parisi, Melissa Sherman-Bennett, Lauren Williams

The hypersimplex ${\Delta }_{k+1,n}$ is the image of the positive Grassmannian $G{r}_{k+1,n}^{\ge 0}$ under the moment map. It is a polytope of dimension $n-1$ in ${\mathbb{R}}^n$. Meanwhile,…