Maximum‐size antichains in random set‐systems1. Issue 2 (19th May 2016) - Collares, Maurício; Morris, Robert
Abstract: We show that, for p n → ∞, the largest set in a p ‐random sub‐family of the power set of { 1, …, n } containing no k ‐chain has size ( k − 1 + o ( 1 ) ) p ( n n / 2 ) with high probability. This confirms a conjecture of Osthus. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 308–321, 2016