Ming-Yu Liu

Forbidden graded posets in middle levels: supersaturation, enumeration and randomness

Let $P$ be a fixed finite poset whose maximal chains all have $h$ elements, and let $\mathcal W_{n,h}$ be the union of $h$ consecutive middle levels of $2^{[n]}$. We prove that the maximum size of a $P$-free subfamily of $\mathcal W_{n,h}$ is $(\pi(P)+o(1))M_n$ for a constant $\pi(P)$, where $M_n=\binom n{\lfloor n/2\r...