The space of maximal convex sets
نویسندگان
چکیده
منابع مشابه
On Maximal S-Free Convex Sets
Let S ⊆ Zn satisfy the property that conv(S) ∩ Zn = S. Then a convex set K is called an S-free convex set if int(K) ∩ S = ∅. A maximal S-free convex set is an S-free convex set that is not properly contained in any S-free convex set. We show that maximal S-free convex sets are polyhedra. This result generalizes a result of Basu et al. [6] for the case where S is the set of integer points in a r...
متن کاملOn Maximal S-free Convex Sets
Let S ⊆ Zn satisfy the property that conv(S) ∩ Zn = S. Then a convex set K is called an S-free convex set if int(K) ∩ S = ∅. A maximal S-free convex set is an S-free convex set that is not properly contained in any S-free convex set. We show that maximal S-free convex sets are polyhedra. This result generalizes a result of Basu et al. [6] for the case where S is the set of integer points in a r...
متن کاملMaximal S-Free Convex Sets and the Helly Number
Given a subset S of R, the Helly number h(S) is the largest size of an inclusionwise minimal family of convex sets whose intersection is disjoint from S. A convex set is S-free if its interior contains no point of S. The parameter f(S) is the largest number of maximal faces in an inclusionwise maximal S-free convex set. We study the relation between the parameters h(S) and f(S). Our main result...
متن کاملOn Maximal S-Free Sets and the Helly Number for the Family of S-Convex Sets
We study two combinatorial parameters, which we denote by f(S) and h(S), associated with an arbitrary set S ⊆ Rd, where d ∈ N. In the nondegenerate situation, f(S) is the largest possible number of facets of a d-dimensional polyhedron L such that the interior of L is disjoint with S and L is inclusion-maximal with respect to this property. The parameter h(S) is the Helly number of the family of...
متن کاملMaximal Lattice-Free Convex Sets in Linear Subspaces
We consider a model that arises in integer programming, and show that all irredundant inequalities are obtained from maximal lattice-free convex sets in an affine subspace. We also show that these sets are polyhedra. The latter result extends a theorem of Lovász characterizing maximal lattice-free convex sets in R.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1981
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-111-1-45-59