On a Convex Operator for Finite Sets

Details On a Convex Operator for Finite Sets On a Convex Operator for Finite Sets

2006-06-15

arxiv.org/abs/math/0606371v1

Mathematics

Metric Geometry

20 pages, 16 figures

Scientific paper

Let $S$ be a finite set with $n$ elements in a real linear space. Let $\cJ_S$ be a set of $n$ intervals in $\nR$. We introduce a convex operator $\co(S,\cJ_S)$ which generalizes the familiar concepts of the convex hull $\conv S$ and the affine hull $\aff S$ of $S$. We establish basic properties of this operator. It is proved that each homothet of $\conv S$ that is contained in $\aff S$ can be obtained using this operator. A variety of convex subsets of $\aff S$ can also be obtained. For example, this operator assigns a regular dodecagon to the 4-element set consisting of the vertices and the orthocenter of an equilateral triangle. For $\cJ_S$ which consists of bounded intervals, we give the upper bound for the number of vertices of the polytope $\co(S,\cJ_S)$.

Affiliated with

Also associated with

No associations

Rating

On a Convex Operator for Finite Sets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On a Convex Operator for Finite Sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On a Convex Operator for Finite Sets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-606908