✦ LIBER ✦
On the Size of Set Systems on [n] Not Containing Weak (r, Δ)-Systems
✍ Scribed by Vojtěch Rödl; Luboš Thoma
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 286 KB
- Volume
- 80
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
✦ Synopsis
Let r 3 be an integer. A weak (r, 2)-system is a family of r sets such that all pairwise intersections among the members have the same cardinality. We show that for n large enough, there exists a family F of subsets of [n] such that F does not contain a weak (r, 2)-system and |F| 2 (1Â3) } n 1Â5 log 4Â5 (r&1) . This improves an earlier