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arXiv · 1404.5258

Maximum-size antichains in random set-systems

Maurício Collares Neto·Robert Morris
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Abstract

We show that, for $pn \to \infty$, the largest set in a $p$-random sub-family of the power set of $\{1, \ldots, n\}$ containing no $k$-chain has size $( k - 1 + o(1) ) p \binom{n}{n/2}$ with high probability. This confirms a conjecture of Osthus, and has been proved independently by Balogh, Mycroft and Treglown.

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Maurício Collares Neto, Robert Morris. 2015-11-12. Maximum-size antichains in random set-systems. https://arxiv.org/abs/1404.5258

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