Hong Liu

activity

20232026

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9 papers · 1 filter

math.CO2026

Colored Turán densities and finite directed templates

Nannan Chen, Ander Lamaison, Heng Li +1

Classical Turán theory relates the asymptotic extremal problem for an ordinary forbidden graph to its chromatic number. This principle fails when a forbidden copy must respect pres…

math.CO2026

Solution of uniform Turán's Tetrahedron Problem

Bartłomiej Kielak, Daniel Král, Ander Lamaison +3

Turán's Tetrahedron Problem asks to determine the Turán density of the complete hypergraph $K_{4}^{(3)}$ (tetrahedron). This problem, posed by Turán in 1941, is one of the most famou…

math.CO2026

Upper-shadow comparisons on the slice and the Frankl--Tokushige product conjectures

Fan Chang, Hong Liu, Miao Liu

Let $F \subseteq (k [ n ])$ , and let $\partial_{k \to ℓ} F$ be the family of all $ℓ$ -sets containing a member of $F$ . Writing $μ_k(\mathcal{F})=|\…

math.CO2026

A Higher-Order Clique Density Theorem

Heng Li, Hong Liu, Yixiao Zhang

Reiher's clique density theorem determines the sharp lower envelope for the density of $K_{r}$ at fixed edge density. We prove a higher-order version in which the prescribed quantity…

math.CO2026

Tree suspensions and transfer functions for single degree Turán spectra

Jiangdong Ai, Laihao Ding, Hong Liu +1

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

math.CO2026

The sharp diagonal spectral correlation inequality on the discrete cube

Fan Chang, Hong Liu, Miao Liu

We prove the sharp diagonal spectral correlation conjecture of Friedgut, Kahn, Kalai and Keller, proposed in their Fourier-analytic approach to Chvátal's conjecture. For every pair…

math.CO2026

A sharp $p$ -biased product bound for $r$ -cross-intersecting families

Fan Chang, Hong Liu, Miao Liu

We prove a sharp product theorem for $r$ -cross-intersecting families in the $p$ -biased measure. If $r \geq 2$ , $0 \leq p \leq \frac{r - 1}{r}$ , and $\mathcal{F}_1,\dots,\mathcal{F}_r\subset…

math.CO2026

A dichotomy for hypergraph Zarankiewicz problems on axis-parallel boxes

Ting-Wei Chao, Zichao Dong, Hong Liu +2

We study the Zarankiewicz problem for $r$ -partite, $r$ -uniform intersection hypergraphs arising from $r$ families of axis-parallel boxes in $R^{d}$ with prescribed direction…

math.CO2026

Vanishing orders, suspensions and zero degree Turán densities

Jiangdong Ai, Laihao Ding, Hong Liu +1

For integers $1 \leq ℓ < k$ , the $ℓ$ -degree Turán density $π_{ℓ} (F)$ measures the minimum $ℓ$ -degree threshold that forces a copy of a fixed $k$ -uniform hypergraph $F$ , gener…

Colored Turán densities and finite directed templates

Solution of uniform Turán's Tetrahedron Problem

Upper-shadow comparisons on the slice and the Frankl--Tokushige product conjectures

A Higher-Order Clique Density Theorem

Tree suspensions and transfer functions for single degree Turán spectra

The sharp diagonal spectral correlation inequality on the discrete cube

A sharp p-biased product bound for r-cross-intersecting families

A dichotomy for hypergraph Zarankiewicz problems on axis-parallel boxes

Vanishing orders, suspensions and zero degree Turán densities

A sharp $p$ -biased product bound for $r$ -cross-intersecting families