Maximum-size antichains in random set-systems

Maurício Collares Neto; Robert Morris

Maximum-size antichains in random set-systems

Combinatorics 2015-11-13 v3

Authors: Maurício Collares Neto , Robert Morris

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.

Keywords

intersecting families

Cite

@article{arxiv.1404.5258,
  title  = {Maximum-size antichains in random set-systems},
  author = {Maurício Collares Neto and Robert Morris},
  journal= {arXiv preprint arXiv:1404.5258},
  year   = {2015}
}

Comments

14 pages, added important observation to the Introduction

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