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The t-intersection Problem in the Truncated Boolean Lattice

✍ Scribed by Rudolf Ahlswede; Christian Bey; Konrad Engel; Levon H. Khachatrian

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 146 KB
Volume: 23
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.2002.0590

No coin nor oath required. For personal study only.

✦ Synopsis

Let I (n, t) be the class of all t-intersecting families of subsets of [n] and set

≤k . After the maximal families in I (n, t) [13] and in I k (n, t) [1,9] are known we study now maximal families in I ≤k (n, t). We present a conjecture about the maximal cardinalities and prove it in several cases.

More generally cardinalities are replaced by weights and asymptotic estimates are given. Analogous investigations are made for I (n, t) ∩ C(n, s), where C(n, s) is the class of all s-cointersecting families of subsets of [n]. In particular we establish an asymptotic form of a conjecture by Bang et al. [4].

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