K-set (geometry)

Summary

In discrete geometry, a $k$-set of a finite point set $S$ in the Euclidean plane is a subset of $k$ elements of $S$ that can be strictly separated from the remaining points by a line. More generally, in Euclidean space of higher dimensions, a $k$-set of a finite point set is a subset of $k$ elements that can be separated from the remaining points by a hyperplane. In particular, when $k=n/2$ (where $n$ is the size of $S$), the line or hyperplane that separates a $k$-set from the rest of $S$ is a halving line or halving plane.