# Anti-chain

From Encyclopedia of Mathematics

2010 Mathematics Subject Classification: *Primary:* 06A06 [MSN][ZBL]

*Sperner family*

A set $A$ of elements of a partially ordered set $(S,\le)$ which are incomparable: for $x \neq y$ in $A$, neither $x \le y$ nor $y \le x$ holds. The width of a partially ordered set is the the largest size of an antichain.

A *Sperner family* is a collection of sets which form an anti-chain with respect to set inclusion. See also Sperner property.

**How to Cite This Entry:**

Anti-chain.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Anti-chain&oldid=39319