2018/04/16 by Nick Early, Early, Nick
Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #High Energy Physics - Theory (hep-th) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1804.05460
openalex publication_date 2018/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
In this note, we study the permutohedral geometry of the poles of a certain differential form introduced in recent work of Arkani-Hamed, Bai, He and Yan. There it was observed that the poles of the form determine a family of polyhedra which have the same face lattice as that of the permutohedron. We realize that family explicitly, proving that it in fact fills out the configuration space of a particularly well-behaved family of generalized permutohedra, the zonotopal generalized permutohedra, that are obtained as the Minkowski sums of line segments parallel to the root directions ei-ej. Finally we interpret Mizera's formula for the biadjoint scalar amplitude m(\mathbbIn,\mathbbIn), restricted to a certain dimension n-2 subspace of the kinematic space, as a sum over the boundary components of the standard root cone, which is the conical hull of the roots e1-e2,…, en-2-en-1.