Some geometric probability problems involving the Eulerian numbers.
Some subpolytopes of the Birkhoff polytope.
Staircase Kernels for Orthogonal d-Polytopes.
Star polytopes and the Schläfli function f(..., ..., ...).
Sur la classification des hexagones hyperboliques à angles droits en dimension 5
The aim of this paper is to give a classification of the right-angled hyperbolic hexagons in the real hyperbolic space , by using a quaternionic distance between geodesics in .
Sur les substitution linéaires
The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings
In 1994, Sturmfels gave a polyhedral version of the Cayley Trick of elimination theory: he established an order-preserving bijection between the posets of coherent mixed subdivisions of a Minkowski sum of point configurations and of coherent polyhedral subdivisions of the associated Cayley embedding . In this paper we extend this correspondence in a natural way to cover also non-coherent subdivisions. As an application, we show that the Cayley Trick combined with results of Santos on subdivisions...
The Cayley–Menger determinant is irreducible for .
The centers of gravity of the associahedron and of the permutahedron are the same.
The Cubical d-Polytopes with Fewer than 2d+1 Vertices.
The generalized Baues problem for cyclic polytopes. II.
The Mayer-Vietoris and IC Equations for Convex Polytopes.
The partition problem for equifacetal simplices.
The semiregualr polytopes.
Triangulations of integral polytopes and Ehrhart polynomials.
Triangulations of simplicial polytopes.
Tropical convexity.
Über die Symmetriegruppen von regulärseitigen Polytopen.
Ueber ein Princip der Zuordnung algebraischer Formen.
Uniform decompositions of polytopes
We design a method of decomposing convex polytopes into simpler polytopes. This decomposition yields a way of calculating exactly the volume of the polytope, or, more generally, multiple integrals over the polytope, which is equivalent to the way suggested in Schechter, based on Fourier-Motzkin elimination (Schrijver). Our method is applicable for finding uniform decompositions of certain natural families of polytopes. Moreover, this allows us to find algorithmically an analytic expression for the...