Miao Liu

collaborators

5 papers

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

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 ChvÃ¡tal's conjecture. For every pai…

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

Sharp asymptotic bounds for uniform union-free hypergraphs

Miao Liu, Chong Shangguan, Chenyang Zhang

An $r$ -uniform hypergraph is called $t$ -union-free if any two distinct subsets of at most $t$ edges have distinct union. The study of union-free hypergraphs has multiple origins an…

math.CO2024

Asymptotically sharp bounds for cancellative and union-free hypergraphs

Miao Liu, Chong Shangguan, Chenyang Zhang

An $r$ -graph is called $t$ -cancellative if for arbitrary $t + 2$ distinct edges $A_{1}, \dots, A_{t}, B, C$ , it holds that $(\cup_{i = 1}^{t} A_{i}) \cup B \neq = (\cup_{i = 1}^{t} A_{i}) \cup C$ ; it is cal…

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

The sharp diagonal spectral correlation inequality on the discrete cube

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

Sharp asymptotic bounds for uniform union-free hypergraphs

Asymptotically sharp bounds for cancellative and union-free hypergraphs

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