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Difference between revisions of "Anti-chain"

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''Sperner family''
 
''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.
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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 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=39319