Difference between revisions of "Anti-chain"
From Encyclopedia of Mathematics
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| − | 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 | + | 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]]. | A ''Sperner family'' is a collection of sets which form an anti-chain with respect to set inclusion. See also [[Sperner property]]. | ||
Latest revision as of 12:24, 12 December 2020
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 $x \le y$ 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
Anti-chain. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Anti-chain&oldid=50957