Cut family
In mathematics, an intersection family of a set describes a family of subsets of , in which two of its elements each have a non-empty intersection.
definition
A set family is called a section family if the following property is met:
- For all true .
Remarks
The maximum thickness of an intersecting family of a finite set of the thickness is .
Each filter is a cut family.
A pattern family describes a pattern family in which all elements have the thickness . Erdős-Ko-Rado's theorem makes a statement about the maximum thicknesses of such families .
According to Kleitman's theorem , the union of intersecting families has at most subsets.
swell
- Martin Aigner , Günter M. Ziegler : The BOOK of evidence . Springer, Berlin 2002, ISBN 3-540-42535-7 (3rd edition: ISBN 978-3-642-02258-6 )
- Stasys Jukna : Extremal Combinatorics. Springer, Berlin 2001, ISBN 3-540-66313-4 .
Individual evidence
- ↑ Stasys Jukna : Extremal Combinatorics. Springer, Berlin 2001, ISBN 3-540-66313-4 , p. 90.
- ↑ Stasys Jukna : Extremal Combinatorics. Springer, Berlin 2001, ISBN 3-540-66313-4 , p. 91.