The Width of Random Subsets of Boolean Lattices

Suppose we toss an independent coin with probability of success p for each subset of [n] = {1, . . . , n}, and form the random hypergraph P(n, p) by taking as hyperedges the subsets with successful coin tosses. We investigate the cardinality of the largest Sperner family contained in P(n, p). We obtain a sharp result for the range of p = p(n) in which this Sperner family has cardinality comparable to the cardinality of P(n, p).

• Type: Journal
• Year: 2002
• Where: JCT
• Authors: Yoshiharu Kohayakawa, Bernd Kreuter
• Keywords: Independent Coin, JCT 2002, Sperner Family, Successful Coin Tosses