منابع مشابه
Delaunay polytopes of cut lattices
We continue 3], the study of the lattice L n generated by cuts of the complete graph on a set V n of n vertices. The lattice L n spans an N = ? n 2-dimensional space of all functions deened on a set V 2 n of all unordered pairs of the set V n. We prove that the cut polytope, i.e. the convex hull of all cuts, is an asymmetric Delaunay polytope of L n. Symmetric Delaunay polytopes of a lattice L ...
متن کاملThe even and odd cut polytopes
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 ...
متن کاملThe volume of relaxed Boolean-quadric and cut polytopes
For n 2, the boolean quadric polytope P n is the convex hull in d := ? n+1 2 dimensions of the binary solutions of x i x j = y ij , for all i < j in N := f1; 2; :::; ng. The polytope is naturally modeled by a somewhat larger polytope; namely, Q n the solution set of y ij x i , y ij x j , x i + x j 1 + y ij , y ij 0, for all i; j in N. In a rst step toward seeing how well Q n approximates P n , ...
متن کاملLattice polytopes cut out by root systems and the Koszul property
We show that lattice polytopes cut out by root systems of classical type are normal and Koszul, generalizing a well-known result of Bruns, Gubeladze, and Trung in type A. We prove similar results for Cayley sums of collections of polytopes whose Minkowski sums are cut out by root systems. The proofs are based on a combinatorial characterization of diagonally split toric varieties.
متن کاملStabbing simplices by points and flats
The following result was proved by Bárány in 1982: For every d ≥ 1 there exists cd > 0 such that for every n-point set S in R d there is a point p ∈ R contained in at least cdn d+1 −O(n) of the d-dimensional simplices spanned by S. We investigate the largest possible value of cd. It was known that cd ≤ 1/(2(d+ 1)!) (this estimate actually holds for every point set S). We construct sets showing ...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1995
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02570706