Add to ORKGGiven a polyhedron P subset R n we write P I for the convex hull of the integral points in P. It is known that P I can have at most O(ϕ n-1 ) vertices if P is a rational polyhedron with size ϕ. Here we give an example showing that P I can have as many as Ω(ϕ n-1 ) vertices. The construction uses the Dirichlet unit theorem
The classical Steinitz theorem states that if the origin belongs to the interior of the convex hull ...
AbstractLet Bn be a hyperball in Rn, n≥2, and denote BZn=Bn∩Zn. Define polyhedral facet complexity o...
Gomory's and Chvátal's cutting-plane procedure proves recursively the validity of linear inequalit...
We give an upper bound on the number of vertices of PI, the integer hull of a polyhedron P, in terms...
Let P r denote the convex hull of the integer points in the disc of radius r . We prove that the num...
SIGLEAvailable from Bibliothek des Instituts fuer Weltwirtschaft, ZBW, Duesternbrook Weg 120, D-2410...
Abstract. We give a lower bound for the number of vertices of a general d-dimensional polytope with ...
In this note we give upper bounds for the number of vertices of the polyhedron $P(A,b) = \{x \in Rd:...
We show that maximal S-free convex sets are polyhedra when S is the set of integral points in some r...
interpretation. Polyhedral analysis is effective when the relationships be-tween variables are linea...
We show that maximal S-free convex sets are polyhedra when S is the set of integral points in some r...
We give a lower bound for the number of vertices of a general d-dimensional polytope with a given nu...
This thesis presents solutions to various problems in the expanding field of combinatorial geometry....
Gomory’s and Chvátal’s cutting-plane procedure proves recursively the validity of linear inequalitie...
For a d-dimensional polytope with v vertices, d + 1 = 0.62d. This confirms a conjecture of Grunbaum,...
The classical Steinitz theorem states that if the origin belongs to the interior of the convex hull ...
AbstractLet Bn be a hyperball in Rn, n≥2, and denote BZn=Bn∩Zn. Define polyhedral facet complexity o...
Gomory's and Chvátal's cutting-plane procedure proves recursively the validity of linear inequalit...
We give an upper bound on the number of vertices of PI, the integer hull of a polyhedron P, in terms...
Let P r denote the convex hull of the integer points in the disc of radius r . We prove that the num...
SIGLEAvailable from Bibliothek des Instituts fuer Weltwirtschaft, ZBW, Duesternbrook Weg 120, D-2410...
Abstract. We give a lower bound for the number of vertices of a general d-dimensional polytope with ...
In this note we give upper bounds for the number of vertices of the polyhedron $P(A,b) = \{x \in Rd:...
We show that maximal S-free convex sets are polyhedra when S is the set of integral points in some r...
interpretation. Polyhedral analysis is effective when the relationships be-tween variables are linea...
We show that maximal S-free convex sets are polyhedra when S is the set of integral points in some r...
We give a lower bound for the number of vertices of a general d-dimensional polytope with a given nu...
This thesis presents solutions to various problems in the expanding field of combinatorial geometry....
Gomory’s and Chvátal’s cutting-plane procedure proves recursively the validity of linear inequalitie...
For a d-dimensional polytope with v vertices, d + 1 = 0.62d. This confirms a conjecture of Grunbaum,...
The classical Steinitz theorem states that if the origin belongs to the interior of the convex hull ...
AbstractLet Bn be a hyperball in Rn, n≥2, and denote BZn=Bn∩Zn. Define polyhedral facet complexity o...
Gomory's and Chvátal's cutting-plane procedure proves recursively the validity of linear inequalit...