The packing density of the regular cross-polytope in Euclidean n-space is unknown except in dimensions 2 and 4 where it is 1. The only non-trivial upper bound is due to Gravel, Elser, and Kallus [9] who proved that for n = 3 the packing density of the regular octahedron is at most 1 − 1.4 . . .× 10. In this paper, we prove upper bounds for the packing density of the n-dimensional regular cross-...

Deriving the form of the optimal solution of a maximum entropy problem, we obtain an infinite family of linear inequalities characterizing the polytope of spin correlation matrices. For n ≤ 6, the facet description of such a polytope is provided through a minimal system of Bell-type inequalities.

It is well known that the set of correlated equilibrium distributions of an n-player noncooperative game is a convex polytope that includes all the Nash equilibrium distributions. We demonstrate an elementary yet surprising result: the Nash equilibria all lie on the boundary of the polytope. JEL Classification: C720.

The tensorial Bernstein basis for multivariate polynomials in n variables has a number 3n of functions for degree 2. Consequently, computing the representation of a multivariate polynomial in the tensorial Bernstein basis is an exponential time algorithm, which makes tensorial Bernstein-based solvers impractical for systems with more than n= 6 or 7 variables. This article describes a polytope (...

a compact formulation of the set of tours neither in a graph nor its complement is presented and illustrates a general methodology proposed for constructing polyhedral models of decision problems based upon permutations, projection and lifting techniques. directed hamilton tours on n vertex graphs are interpreted as (n-1)- permutations. sets of extrema of birkhoff polyhedra are mapped to tours ...

While it was known for a long time how to transform an asymmetric traveling salesman problem on the complete graph with n vertices into a symmetric traveling salesman problem on an incomplete graph with 2n vertices, no method was available until recently for using this correspondence to derive facets of the symmetric traveling salesman polytope from facets of the asymmetric one. In this paper w...

j=1 cijxij s. t. 0 6 xij 6 1, xij + xji = 1, 0 6 xij + xjk − xik 6 1, i 6= j, i 6= k, j 6= k, i, j, k = 1, ..., n. We denote the corresponding polytope by Bn. The polytope Bn has integer vertices corresponding to feasible solutions of the linear ordering problem as well as non-integer vertices. We denote the polytope of integer vertices as Pn. Let us give an example of non-integer vertex in Bn ...

We describe a perturbation method that can be used to compute the multivariate generating function (MGF) of a non-simple polyhedron, and then construct a perturbation that works for any transportation polytope. Applying this perturbation to the family of central transportation polytopes of order kn × n, we obtain formulas for the MGF of the polytope. The formulas we obtain are enumerated by com...

Deza, M. and M. Laurent, The even and odd cut polytopes, Discrete Mathematics 119 (1993) 49966. The cut polytope P, is the convex hull of the incidence vectors of all cuts of the complete graph K, on n nodes. An even cut is a cut of even cardinality. For n odd, all cuts are even. For n even, we consider the even cut polytope EvP,, defined as the convex hull of the incidence vectors of all even ...