On the density of primitive sets
✍ Scribed by R. Ahlswede; L. Khachatrian; A. Sárközy
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 361 KB
- Volume
- 109
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
✦ Synopsis
Classical results by Behrend, Erdös, Pillai, Szemerédi, the authors, and others are improved and extended to other concepts of densities in two directions, based on smooth and multiplicative weightings.
📜 SIMILAR VOLUMES
Answering a question of Erd6s, Sauer [4] and indepe~dently Pcrles and Shelah [5] found the maximal cardinality of a collection ~ of subsets of a se~: N of cardinality n such that for ever/ subset M ~ N of cardinality m I{C f3 M: C ~ 3b'}l < 2". Karl~)vsky and Milman [3] generalised this result. Here
Consider the lattice of divisors of n, [1, n]. For any downset (ideal) J in [1, n] we get a forbidden configuration theorem of the type that if a set of divisors D avoids certain configurations, then ] D ] ~< I J ]. If we let 5 ¢ be the set of minimal elements of [ 1, n] not in J, then we forbid in