We study subset families of a finite set that come from combinatorial decomposition theories such as graph substitution decomposition, boolean function decomposition, hypergraph or clutter substitution decomposition; see Omningham and Edmonds' paper [6]. We consider these families as ordered sets a
Weighted 3-Wise 2-Intersecting Families
β Scribed by Peter Frankl; Norihide Tokushige
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 190 KB
- Volume
- 100
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
For fixed s, n, k, and t, let I s (n, k, t) denote the set of all such families. A family A # I s (n, k, t) is said to be maximal if it is not properly contained in any other family in I s (n, k, t). We show that for fixed s, k, t, there is an integer n 0 =n 0 (k, s, t), for which the maximal famili
Suppose that any t members (t 2) of a regular family on an n element set have at least k common elements. It is proved that the largest member of the family has at least k 1Γt n 1&1Γt elements. The same holds for balanced families, which is a generalization of the regularity. The estimate is asympto