Related papers: Combinatorics of the Cosmohedron

We introduce (co)homology theory for multiple group racks and construct cocycle invariants of compact oriented surfaces in the 3-sphere using their 2-cocycles, where a multiple group rack is a rack consisting of a disjoint union of groups.…

We present a combinatorial isomorphism between Stasheff associahedra and an inductive cone construction of those complexes given by Loday. We give an alternate description of certain polytopes, known as multiplihedra, which arise in the…

We investigate a family of polytopes introduced by E.M.\ Feichtner, A.\ Postnikov and B.\ Sturmfels, which were named nestohedra. The vertices of these polytopes may intuitively be understood as constructions of hypergraphs. Limit cases in…

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…

We compute the Poisson cohomology of a class of Poisson manifolds that are symplectic away from a collection $D$ of hypersurfaces. These Poisson structures induce a generalization of symplectic and cosymplectic structures, which we call a…

This thesis explores two specific topics of discrete geometry, the multitriangulations and the polytopal realizations of products, whose connection is the problem of finding polytopal realizations of a given combinatorial structure. A…

Brick polytopes constitute a remarkable family of polytopes associated to the spherical subword complexes of Knutson and Miller. They were introduced for finite Coxeter groups by Pilaud and Stump, who used them to produce geometric…

In hep-th/0111053, a complete simplicial fan was associated to an arbitrary finite root system. It was conjectured that this fan is the normal fan of a simple convex polytope (a generalized associahedron of the corresponding type). Here we…

In a previous article, we proved tight lower bounds for the coefficients of the generalized $h$-vector of a centrally symmetric rational polytope using intersection cohomology of the associated projective toric variety. Here we present a…

We observe that a large part of the volume of a hyperbolic polyhedron is taken by a tubular neighbourhood of its boundary, and use this to give a new proof for the finiteness of arithmetic maximal reflection groups following a recent work…

A shape of a combinatorial polytope is a convex embedding into Euclidean space. We provide necessary and sufficient conditions for a piecewise linear map between two shapes of the same polytope to be a compression (respectively a weak…

Using the orthogonal connectedness, we introduce the notion of orthogonal decomposability of convex polytopes and study it in the case of Platonic and Archimedean solids. While doing so, we also encounter polytopes which are not…

We define and study the dual mixed volume rational function of a sequence of polytopes, a dual version of the mixed volume polynomial. This concept has direct relations to the adjoint polynomials and the canonical forms of polytopes. We…

In this paper we study the ring $\mathcal{P}$ of combinatorial convex polytopes. We introduce the algebra of operators $\mathcal{D}$ generated by the operators $d_k$ that send an $n$-dimensional polytope $P^n$ to the sum of all its…

This work presents the tessellations and polytopes from the perspective of both n-dimensional geometry and abstract symmetry groups. It starts with a brief introduction to the terminology and a short motivation. In the first part, it…

We introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy their important properties. Moreover, they exist in…

This paper introduces an algebraic combinatorial approach to simplicial cone decompositions, a key step in solving inhomogeneous linear Diophantine systems and counting lattice points in polytopes. We use constant term manipulation on the…

We survey three settings in which dimensions of intersection cohomology groups of algebraic varieties provide deep combinatorial and representation-theoretic information, and computations of the groups themselves have been made using…

A polyhedron is pointed if it contains at least one vertex. Every pointed polyhedron P in R^n can be described by an H-representation consisting of half spaces or equivalently by a V-representation consisting of the convex hull of a set of…

We show that accordiohedra furnish polytopes which encode amplitudes for all massive scalar field theories with generic interactions. This is done by deriving integral formulae for the Feynman diagrams at tree level and integrands at one…