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Balancing families of sets

✍ Scribed by John E Olson; Joel H Spencer


Publisher
Elsevier Science
Year
1978
Tongue
English
Weight
381 KB
Volume
25
Category
Article
ISSN
0097-3165

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πŸ“œ SIMILAR VOLUMES


Intersecting Balanced Families of Sets
✍ Adam Idzik; Gyula O.H. Katona; Rajiv Vohra πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 117 KB

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 1Γ‚t n 1&1Γ‚t elements. The same holds for balanced families, which is a generalization of the regularity. The estimate is asympto

Equidistant families of sets
✍ Yury J. Ionin; Mohan S. Shrikhande πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 797 KB
On families of intersecting sets
✍ Andrzej Ehrenfeucht; Jan Mycielski πŸ“‚ Article πŸ“… 1974 πŸ› Elsevier Science 🌐 English βš– 81 KB
Union-closed families of sets
✍ Piotr WΓ³jcik πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 532 KB

We use a lower bound on the number of small sets in an idea1 to show that for each unionclosed family of n sets there exists an element which belongs to at least of them, provided n is large enough.

Cancellative pairs of families of sets
✍ Ron Holzman; JΓ‘nos KΓΆrner πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 198 KB