Abstract
A disjoint system of type (∀, ∃, k, n) is a collection 𝒞 = {𝒜1,…, 𝒜m} of pairwise disjoint families of k‐subsets of an n‐element set satisfying the following condition. For every ordered pair 𝒜i and 𝒜j of distinct members of 𝒞 and for every A ϵ 𝒜i there exists a B ϵ 𝒜j that does not intersect A. Let Dn (∀, ∃, k) denote the maximum possible cardinality of a disjoint system of type (∀, ∃, k, n). It is shown that for every fixed k ⩾ 2,. (Formula Presented.) This settles a problem of Ahlswede, Cai, and Zhang. Several related problems are considered as well.
Original language | English (US) |
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Pages (from-to) | 13-20 |
Number of pages | 8 |
Journal | Random Structures & Algorithms |
Volume | 6 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1995 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Software
- Mathematics(all)
- Computer Graphics and Computer-Aided Design
- Applied Mathematics