---
tag: W63YT2E5KY
kind: concept
name: K-set (geometry)
aliases: [k-set-mathematics]
sources:
  - wikipedia: en:8075001@r1368661379
    locator: K-set (geometry)
    note: adopted
    mention: wikipedia://en/8075001
    sections: [Summary]
same_as:
  wikidata: Q6322868
  wikipedia: K-set (geometry)
inventory: [TJ5CBZKTAS]
---

## Summary

In discrete geometry, a $k$-set of a finite point set $S$ in the [[Euclidean plane|0XW7V9ZZ05]] is a [[subset|0BJR9QR08E]] of $k$ elements of $S$ that can be strictly separated from the remaining points by a [[line|0MP9BCF6DP]]. More generally, in [[Euclidean space|0XPR1E85W0]] 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**.