A LYM inequality for induced posets

doi:10.1016/j.jcta.2017.11.002

Journal of Combinatorial Theory, Series A

Volume 155, April 2018, Pages 398-417

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Abstract

We prove that for every partially ordered set P, there exists a constant $c (P)$ such that every family $F$ of subsets of $[n]$ ordered by inclusion which contains no induced copy of P satisfies $\sum_{F \in F} 1 / (\begin{matrix} n \\ | F | \end{matrix}) \leq c (P)$ .

Keywords

Forbidden poset

LYM inequality

Strong containment