Optimum basis of finite convex geometry

Largest Extension of a Finite Convex Geometry

We present a new embedding of a finite join-semidistributive lattice into a finite atomistic join-semidistributive lattice. This embedding turns out to be the largest extension, when applied to a finite convex geometry.

Convex Geometry of Orbits

We study metric properties of convex bodies B and their polars B, where B is the convex hull of an orbit under the action of a compact group G. Examples include the Traveling Salesman Polytope in polyhedral combinatorics (G = Sn, the symmetric group), the set of nonnegative polynomials in real algebraic geometry (G = SO(n), the special orthogonal group), and the convex hull of the Grassmannian ...

Convex and Discrete Geometry

Geir Agnarsson, Jill Bigley Dunham.* George Mason University, Fairfax, VA. Extremal coin graphs in the Euclidean plane. A coin graph is a simple geometric intersection graph where the vertices are represented by non-overlapping closed disks in the Euclidean plane and where two vertices are connected if their corresponding disks touch. The problem of determining the maximum number of edges of a ...

Math 341: Convex Geometry

Max-Plus Convex Geometry

Max-plus analogues of linear spaces, convex sets, and polyhedra have appeared in several works. We survey their main geometrical properties, including max-plus versions of the separation theorem, existence of linear and non-linear projectors, max-plus analogues of the Minkowski-Weyl theorem, and the characterization of the analogues of “simplicial” cones in terms of distributive lattices.