Miao Liu

collaborators

8 papers

math.CO2026

Extremal problems for cancellative and locally thin hypergraphs

Miao Liu, Chong Shangguan, Chenyang Zhang

We study Turán-type extremal problems for cancellative and locally thin uniform hypergraphs. An $r$ -uniform hypergraph is $t$ -cancellative if $(\cup_{i=1}^t A_i)\cup B\ne (\cup_{i=…

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 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

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…

cs.IT2024

Near optimal constructions of frameproof codes

Miao Liu, Zengjiao Ma, Chong Shangguan

Frameproof codes are a class of secure codes that were originally introduced in the pioneering work of Boneh and Shaw in the context of digital fingerprinting. They can be used to…

math.CO2024

Approximate generalized Steiner systems and near-optimal constant weight codes

Miao Liu, Chong Shangguan

Constant weight codes (CWCs) and constant composition codes (CCCs) are two important classes of codes that have been studied extensively in both combinatorics and coding theory for…

Extremal problems for cancellative and locally thin hypergraphs

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

Near optimal constructions of frameproof codes

Approximate generalized Steiner systems and near-optimal constant weight codes

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