Anti-chain
From Encyclopedia of Mathematics
Revision as of 19:20, 27 December 2014 by Richard Pinch (talk | contribs) (Start article: Anti-chain)
2020 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 $x \ke y$ 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://encyclopediaofmath.org/index.php?title=Anti-chain&oldid=35892
Anti-chain. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Anti-chain&oldid=35892