Concept

Hyperoctaèdre

Publications associées (8)

On the Volume of the John-Lowner Ellipsoid

We find an optimal upper bound on the volume of the John ellipsoid of a k-dimensional section of the n-dimensional cube, and an optimal lower bound on the volume of the Lowner ellipsoid of a projection of the n-dimensional cross-polytope onto a k-dimension ...

SPRINGER2020

On 2-Level Polytopes Arising In Combinatorial Settings

Yuri Faenza, Manuel Francesco Aprile, Alfonso Bolívar Cevallos Manzano

2-level polytopes naturally appear in several areas of pure and applied mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. In this paper, we present a study of some 2-level polytopes arisi ...

SIAM Publications2018

The mixing time of the Dikin walk in a polytope-A simple proof

Nisheeth Vishnoi

We study the mixing time of the Dikin walk in a polytope a random walk based on the log-barrier from the interior point method literature. This walk, and a close variant, were studied by Narayanan (2016) and Kannan-Narayanan (2012). Bounds on its mixing ti ...

Elsevier Science Bv2016

From Compact Semi-Toric Systems To Hamiltonian S-1-Spaces

Silvia Sabatini

We show how any labeled convex polygon associated to a compact semi-toric system, as de fined by V (u) over tilde Ngoc, determines Karshon's labeled directed graph which classifies the underlying Hamiltonian S-1-space up to isomorphism. Then we characteriz ...

Amer Inst Mathematical Sciences2015

Obstacles For Splitting Multidimensional Necklaces

Michal Lason

The well-known "necklace splitting theorem" of Alon (1987) asserts that every k-colored necklace can be fairly split into q parts using at most t cuts, provided k(q - 1)

Amer Mathematical Soc2015

Weakly regular subdivisions

Lionel Pournin

It is shown that 2-dimensional subdivisions can be made regular by moving their vertices within parallel 1-dimensional spaces. As a consequence, any 2-dimensional subdivision is projected from the boundary complex of a 4-polytope. ...

Springer-Verlag2012

Belt distance between facets of space-filling zonotopes

To every d-dimensional polytope P with centrally symmetric facets one can assign a “subway map” such that every line of this “subway” contains exactly the facets parallel to one of the ridges of P. The belt diameter of P is the maximum number of subway lin ...

2012

Application of the superspace approach to members of the ferrite family

Ivan Orlov

The superspace concept is a new crystallographic approach for the generalisation of symmetry, structural models and structure dependent properties. Although the original motivation for the superspace was intended to describe symmetry of aperiodic crystals, ...

EPFL2007