Year: 2014
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Neto, Maurício Collares, Morris, Robert
Institution: Instituto Nacional de Matemática Pura e Aplicada
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G6126895943
OpenAlex ID: W2952292123