Jiangdong Ai

activity

20242026

collaborators

9 papers

math.CO2026

An improved finite bound for oriented trees in tournaments

Jiangdong Ai, Xiaopan Lian

Sumner's universal tournament conjecture asserts that every tournament on $2 n - 2$ vertices contains every oriented tree on $n$ vertices. Let $f (n)$ be the least integer $N$ such tha…

math.CO2026

Triangular cutoff threshold for the inversion walk on tournaments and the state space of restricted inversions

Jiangdong Ai

Given a labelled tournament on $[n]$ , \emph{inverting} a vertex subset $X$ means reversing every edge with both endpoints in $X$ . Alon, Powierski, Savery, Scott, and Wilmer~\cite{A…

math.CO2026

Tree suspensions and transfer functions for single degree TurÃ¡n spectra

Jiangdong Ai, Laihao Ding, Hong Liu +1

For integers $1 \leq ℓ < k$ , let $I^_{ℓ}^{k}$ denote the single-forbidden $ℓ$ -degree TurÃ¡n spectrum of $k$ -uniform hypergraphs. We introduce transfer functions for this spectrum:…

math.CO2026

Vanishing orders, suspensions and zero degree TurÃ¡n densities

Jiangdong Ai, Laihao Ding, Hong Liu +1

For integers $1 \leq ℓ < k$ , the $ℓ$ -degree TurÃ¡n density $I ¨ _{ℓ} (F)$ measures the minimum $ℓ$ -degree threshold that forces a copy of a fixed $k$ -uniform hypergraph $F$ , gen…

math.CO2026

Maximizing the Steklov eigenvalues on trees with a diameter constraint

Jiangdong Ai, Huiqiu Lin, Yongtang Shi

We study the first nonzero Steklov eigenvalue $I^»_{2} (T, I^´ I^c ◯)$ of the Dirichlet-to-Neumann operator on a finite tree $T$ with leaf boundary $I^´ I^c ◯$ , under a constraint on the diameter…

math.CO2026

Effect of edge-stretching on Steklov eigenvalues and sharp Steklov eigenvalue bounds on leaf--boundary trees

Jiangdong Ai, Yizhe Ji, Xiaopan Lian +1

Let $T$ be a finite tree with leaf set $\dO$ as the boundary and let $I^»_{2}$ be the first nontrivial Steklov eigenvalue. Let $D$ and $ℓ$ be the maximum vertex degree and the numb…