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The length of random subsets of Boolean lattices

✍ Scribed by Y. Kohayakawa; B. Kreuter; D. Osthus

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
236 KB
Volume
16
Category
Article
ISSN
1042-9832

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✦ Synopsis

We form the random poset P P n, p by including each subset of n s 1, . . . , n with probability p and ordering the subsets by inclusion. We investigate the length of the Ε½ . longest chain contained in P P n, p . For p G ern we obtain the limit distribution of this random variable. For smaller p we give thresholds for the existence of chains which imply Ε½ . Ε½ . that almost surely the length of P P n, p is asymptotically n log n y log log 1rp rlog 1rp.

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