Search Results for ""

Let Delta denote an integral convex polytope of dimension n in a lattice M, and let l_Delta(k) denote the number of lattice points in Delta dilated by a factor of the integer ...

A set in R^d is concave if it does not contain all the line segments connecting any pair of its points. If the set does contain all the line segments, it is called convex.

Each centered convex body of sufficiently high dimension has an "almost spherical" k-dimensional central section.

Any set of n+2 points in R^n can always be partitioned in two subsets V_1 and V_2 such that the convex hulls of V_1 and V_2 intersect.

Alexandrov's theorem addresses conditions under which a polygon will fold into a convex polyhedron (Malkevitch).

A convex set K is centro-symmetric, sometimes also called centrally symmetric, if it has a center p that bisects every chord of K through p.

A pyramid with a heptagonal base. The heptagonal pyramid is one of the 257 convex octahedra.

Of all convex n-gons of a given perimeter, the one which maximizes area is the regular n-gon.

Given a convex plane region with area A and perimeter p, then |N-A|<p, where N is the number of enclosed lattice points.

A polynomial is called unimodal if the sequence of its coefficients is unimodal. If P(x) is log-convex and Q(x) is unimodal, then P(x)Q(x) is unimodal.