---
tag: SPECV9X1JE
kind: statement
role: proposition
name: Ahlswede–Khachatrian theorem
sources:
  - wikipedia: en:75465176@r1369030983
    locator: Ahlswede–Khachatrian theorem
    note: adopted
    mention: wikipedia://en/75465176
    sections: [Statement]
same_as:
  wikidata: Q123881455
  wikipedia: Ahlswede–Khachatrian theorem
inventory: [4BF3XCE5Z5]
---

## Statement

In extremal set theory, the **Ahlswede–Khachatrian theorem** generalizes the Erdős–Ko–Rado theorem to $t$-intersecting families. Given parameters $n$, $k$ and $t$, it describes the maximum size of a $t$-intersecting family of subsets of $\{1,\dots,n\}$ of size $k$, as well as the families achieving the maximum size.