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Some inequalities concerning random subsets of a set (Corresp.)

โœ Scribed by Hwang, F.; Shepp, L.


Book ID
114636665
Publisher
IEEE
Year
1987
Tongue
English
Weight
448 KB
Volume
33
Category
Article
ISSN
0018-9448

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Maximum Antichains in Random Subsets of
โœ Deryk Osthus ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 125 KB

We consider the random poset P(n, p) which is generated by first selecting each subset of [n]=[1, ..., n] with probability p and then ordering the selected subsets by inclusion. We give asymptotic estimates of the size of the maximum antichain for arbitrary p= p(n). In particular, we prove that if p