Related papers: Self-Polar Polytopes
The rules to write out any one of the linearly independent functions belonging to the infinite set of those in polynomial form that satisfy the sourceless Grad-Shafranov equation as stated in the toroidal-polar coordinate system are…
The cut polytope of a graph $G$ is the convex hull of the indicator vectors of all cuts in $G$ and is closely related to the MaxCut problem. We give the facet-description of cut polytopes of $K_{3,3}$-minor-free graphs and introduce an…
In this paper we study the classification problem of convex lattice ploytopes with respect to given volume or given cardinality.
Polar plumes are seen as elongated objects starting at the solar polar regions. Here, we analyze these objects from a sequence of images taken simultaneously by the three spacecraft telescopes STEREO/EUVI A and B, and SOHO/EIT. We establish…
We study the harmonic polytope, which arose in Ardila, Denham, and Huh's work on the Lagrangian geometry of matroids. We describe its combinatorial structure, showing that it is a $(2n-2)$-dimensional polytope with…
The convex hull of N independent random points chosen on the boundary of a simple polytope in R^n is investigated. Asymptotic formulas for the expected number of vertices and facets, and for the expectation of the volume difference are…
Deleting a hyperplane from a polar space associated with a symplectic polarity we get a specific, symplectic, affine polar space. Similar geometry, called an \afsempol\ arises as a result of generalization of the notion of an alternating…
This paper deals with transportation polytopes in the probability simplex (that is, sets of categorical bivariate probability distributions with prescribed marginals). Information projections between such polytopes are studied, and a…
This paper discusses properties of the graphs of 2-way and 3-way transportation polytopes, in particular, their possible numbers of vertices and their diameters. Our main results include a quadratic bound on the diameter of axial 3-way…
Vector beams are often regarded as non-separable superpositions of spatial and polarization degrees of freedom that satisfy the wave equation. This interpretation ties their polarization structure to their spatial shape. Here, we introduce…
The symmetric edge polytope ($\mathrm{SEP}$) of a finite simple graph $G$ is a centrally symmetric lattice polytope whose vertices are defined by the edges of the graph. Among the information encoded by these polytopes are the symmetries of…
A class of orthogonal polynomials associated with Coulomb wave functions is introduced. These polynomials play a role analogous to that the Lommel polynomials do in the theory of Bessel functions. The measure of orthogonality for this new…
Recent literature posed the problem of characterising the graph degree sequences with exactly one $3$-polytopal (i.e. planar, $3$-connected) realisation. This seems to be a difficult problem in full generality. In this paper, we…
Inspired by Coxeter's notion of Petrie polygon for $d$-polytopes (see \cite{Cox73}), we consider a generalization of the notion of zigzag circuits on complexes and compute the zigzag structure for several interesting families of…
Spatial field correlation functions represent a key quantity for the description of mesoscopic phenomena in disordered media and the optical characterization of complex materials. Yet many aspects related to the vector nature of light waves…
We give compact extended formulations for the packing and partitioning orbitopes (with respect to the full symmetric group) described and analyzed in (Kaibel and Pfetsch, 2008). These polytopes are the convex hulls of all 0/1-matrices with…
Abstract polytopes are a combinatorial generalization of convex and skeletal polytopes. Counting how many flag orbits a polytope has under its automorphism group is a way of measuring how symmetric it is. Polytopes with one flag orbit are…
We analyze self-dual polyhedral cones and prove several properties about their slack matrices. In particular, we show that self-duality is equivalent to the existence of a positive semidefinite (PSD) slack. Beyond that, we show that if the…
A spherical polyhedron surface is a triangulated surface obtained by isometric gluing of spherical triangles. For instance, the boundary of a generic convex polytope in the 3-sphere is a spherical polyhedron surface. This paper investigates…
This work proposes a new model in the context of statistical theory of shape, based on the polar decomposition. The non isotropic noncentral elliptical shape distributions via polar decomposition is derived in the context of zonal…