# Anti-chain

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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 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=50957