On the density of families of sets
β Scribed by N Sauer
- Publisher
- Elsevier Science
- Year
- 1972
- Tongue
- English
- Weight
- 133 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
π 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 Β’ be the set of minimal elements of [ 1, n] not in J, then we forbid in
Grieser, D., Some results on the complexity of families of sets, Discrete Mathematics 88 (1991) 179-192. Let 'Y be a property of graphs on a fixed n-element vertex set V. The complexity c(P) is the minimal number of edges whose existence in a previously unknown graph H has to be tested such that it
Watanabe, M., Arrow relations on families of finite sets, Discrete Mathematics 94 (1991) 53-64. Let n, m and k be positive integers. Let X be a set of cardinality n, and let 9 be a family of subsets of X. We write (n, m)-, (n -1, mk), when for all 9 with (S( em, there exists an element x of X such t