Abstract
A disjoint system of type (โ, โ, k, n) is a collection ๐ = {๐1,โฆ, ๐m} of pairwise disjoint families of kโsubsets of an nโelement set satisfying the following condition. For every ordered pair ๐i and ๐j of distinct members of ๐ and for every A ฯต ๐i there exists a B ฯต ๐j that does not intersect A. Let Dn (โ, โ, k) denote the maximum possible cardinality of a disjoint system of type (โ, โ, k, n). It is shown that for every fixed k โฉพ 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
- General Mathematics
- Computer Graphics and Computer-Aided Design
- Applied Mathematics