Propriétés géométriques liées aux parenthésages d’un produit de facteurs. Application à une loi de composition partielle
Quaternionic geometry of matroids
Building on a recent paper [8], here we argue that the combinatorics of matroids are intimately related to the geometry and topology of toric hyperkähler varieties. We show that just like toric varieties occupy a central role in Stanley’s proof for the necessity of McMullen’s conjecture (or g-inequalities) about the classification of face vectors of simplicial polytopes, the topology of toric hyperkähler varieties leads to new restrictions on face vectors of matroid complexes. Namely in this paper...
Random Projections of Regular Simplices.
Recognizing the topology of the space of closed convex subsets of a Banach space
Remarks on missing faces and generalized lower bounds on face numbers.
Rigidity and the Alexandrov-Fenchel Inequality.
Sections of simplices.
Simple 3-polytopal graphs with edges of only two types and shortness coefficients
Simple Vertices of Maximal Minor Polytopes
Simplicial convex 4-polytopes do not have the isotopy property
Simplicial manifolds, bistellar flips and a 16-vertex triangulation of the Poincaré homology 3-sphere.
Spectra of Regular Polytopes.
Sweeping the cd-index and the toric -vector.
The alternating sign matrix polytope.
The angle defect for arbitrary polyhedra.
The cd-index of Bruhat intervals.
The Lower and Upper Bound Problems for Cubical Polytopes.
The Mayer-Vietoris and IC Equations for Convex Polytopes.
The minimal perimeter for confined deformable bubbles of equal area.
The skeleta of convex bodies
The connectivity and measure theoretic properties of the skeleta of convex bodies in Euclidean space are discussed, together with some long standing problems and recent results.