The amplituhedron \(\mathcal{A}_{n,k,m}\) was introduced by Arkani-Hamed and Trnka (2014) in order to give a geometric basis for calculating scattering amplitudes planar \(\mathcal{N}=4\) supersymmetric Yang-Mills theory. It is projection inside the Grassmannian \(\text{Gr}_{k,k+m}\) of totally nonnegative part \(\text{Gr}_{k,n}\). Karp Williams (2019) studied \(m=1\) \(\mathcal{A}_{n,k,1}\), g...

We present a new approach for the generation of hexahedral finite element meshes for solid bodies in computer-aided design. The key idea is to use a purely combinatorial method, namely a shelling process, to decompose a topological ball with a prescribed surface mesh into combinatorial cubes, so-called hexahedra. The shelling corresponds to a series of graph transformations on the surface mesh ...

In this paper we study the partially ordered set Q of cells in Rietsch’s [20] cell decomposition of the totally nonnegative part of an arbitrary flag variety P ≥0 . Our goal is to understand the geometry of P ≥0 : Lusztig [13] has proved that this space is contractible, but it is unknown whether the closure of each cell is contractible, and whether P ≥0 is homeomorphic to a ball. The order comp...