#### 34 Citations

Table of Contents

- 2004

s, 22nd Symposium on Fusion Technology, Helsinki, Finland, September 2002, 183 (2002) Darbos. C, et al., Alberti S., Tran M.Q., “Very Long Pulse Operation of the TORE Supra ECRH System“, Book of… Expand

Face Numbers of Centrally Symmetric Polytopes Produced from Split Graphs

- Mathematics, Computer Science
- Electron. J. Comb.
- 2013

This study produces a new family of Hansen polytopes that have only $3^d+16$ nonempty faces, and confirms Kalai's $3D$ conjecture for such poly topes and shows that the Hannerpolytopes among them correspond to threshold graphs. Expand

Polytopal balls arising in optimization

- Mathematics
- 2020

We study a family of polytopes and their duals, that appear in various optimization problems as the unit balls for certain norms. These two families interpolate between the hypercube, the unit ball… Expand

15 BASIC PROPERTIES OF CONVEX POLYTOPES

- 2017

Convex polytopes are fundamental geometric objects that have been investigated since antiquity. The beauty of their theory is nowadays complemented by their importance for many other mathematical… Expand

Constructions and obstructions for extremal polytopes

- Engineering
- 2008

In the fall of 2001, I was finishing my computer science undergrad studies and Martin Skutella suggested that I take the course " Linear optimization " , a course offered to beginning math grad… Expand

Nonexpansive maps with surjective displacement

- Mathematics
- 2021

We investigate necessary and sufficient conditions for a nonexpansive map f on a Banach space X to have surjective displacement, that is, for f − id to map onto X. In particular, we give a computable… Expand

Isocanted alcoved polytopes

- Mathematics
- 2020

Through tropical normal idempotent matrices, we introduce isocanted alcoved polytopes, computing their $f$--vectors and checking the validity of the following five conjectures: Barany, unimodality,… Expand

A Tale of Centrally Symmetric Polytopes and Spheres

- Mathematics
- Association for Women in Mathematics Series
- 2019

This paper is a survey of recent advances as well as open problems in the study of face numbers of centrally symmetric simplicial polytopes and spheres. The topics discussed range from neighborliness… Expand

Enumeration of 2-level polytopes

- Mathematics, Computer Science
- Math. Program. Comput.
- 2019

This paper presents the first algorithm for enumerating all combinatorial types of 2-level polytopes of a given dimension d, and provides complete experimental results for d⩽7. Expand

#### References

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On the number of faces of centrally-symmetric simplicial polytopes

- Mathematics, Computer Science
- Graphs Comb.
- 1987

The conjectures of Björner are proved and generalizes the result of Bárány-Lovász sincefd−1 =∑ hi, and more strongly that h_i - h_{i - 1} \geqslant \left( {\begin{array}{*{20}c} d \\ i \\ \end{array} } \right) . Expand

Une Caracterisation Volumique de Certains Espaces Normes de Dimension Finie

- Mathematics
- 1986

We give a geometric characterization of finite dimensional normed spacesE, with a 1-unconditional basis, such that their volumetric product is minimal.

Borsuk's theorem and the number of facets of centrally symmetric polytopes

- Mathematics
- 1982

Let C"={x~R": Ix~]<-i i=1 , . . . ,n} be the n-dimensional cube and A be a d-dimensional subspace of R" having no point in common with the ( n d 1 ) dimensional faces of C". We want to find a lower… Expand

The structure of finite dimensional Banach spaces with the 3.2. Intersection property

- Mathematics
- 1981

Let X be a Banach space over the real numbers. Let n and k be integers with 2 ~< k < n. We say tha t X has the n.k. intersection property (n.k.I.P.) if the following holds: Any n balls in X intersect… Expand

The dimension of almost spherical sections of convex bodies

- Mathematics
- 1977

© Séminaire analyse fonctionnelle (dit "Maurey-Schwartz") (École Polytechnique), 1975-1976, tous droits réservés. L’accès aux archives du séminaire d’analyse fonctionnelle implique l’accord avec les… Expand