Author

Jiangdong Ai

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Preprint Oct 2026

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...

Jiang-Dong Ai, Ming-Yu Liu, Zhi-Yu Song · 0 citations

Preprint Aug 2026

An improved finite bound for oriented trees in tournaments

Sumner's universal tournament conjecture asserts that every tournament on $2n-2$ vertices contains every oriented tree on $n$ vertices. Let $f(n)$ be the least integer $N$ such that every tournament on $N$ vertices contains every oriented tree on $n$ vertices. Havet and Thomass\'e proved that $f(n)\le \lceil(7n-5)/2\rc...

Jiangdong Ai, Xiao-Pan Lian · 1 citation