Lu Lu

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math.CO2026

A Spectral Hilton--Milner--Frankl Theorem for $t$ -Intersecting Families

Xucheng Bu, Lihua Feng, Lu Lu +1

Keevash, Lenz, and Mubayi proved a spectral Erdős--Ko--Rado theorem, showing that, for sufficiently large $n$ , the complete $t$ -star uniquely maximizes the adjacency-tensor spectra…

math.CO2026

An improved range for the maximum critically $t$ -intersecting hypergraphs

Lu Lu, Rongrong Lu, Qifan Wang +1

Let $k > t \geq 1$ be integers and set $d = k - t$ . A $k$ -uniform hypergraph $F$ is called $t$ -intersecting if any two edges intersect in at least $t$ vertices, and is called $t$ -…

math.CO2026

The Second Largest Eigenvalue of Stiffness Matrices of Normalized Complete Frameworks

Tingting Wang, Lu Lu

Let $R (G, p)$ be the normalized rigidity matrix of a framework $(G, p)$ in $R^{d}$ , and let \[ L(G,p)=R(G,p)R(G,p)^{T} \] be the associated stiffness matrix. We study the extre…

math.CO2026

Thresholds for the Frankl-Wang $3/7$ conjecture on maximum-degree ratios

Zejun Huang, Zhiyi Liu, Lu Lu +1

Let $F \subset (k [ n ])$ be an intersecting family, $Δ (F) = max_{x \in [n]} ∣ {F \in F : x \in F} ∣$ , and $\varrho(\mathcal{F})=Δ(\mathcal{F})/|\mathcal{F}…

A Spectral Hilton--Milner--Frankl Theorem for t-Intersecting Families

An improved range for the maximum critically t-intersecting hypergraphs

The Second Largest Eigenvalue of Stiffness Matrices of Normalized Complete Frameworks

Thresholds for the Frankl-Wang 3/7 conjecture on maximum-degree ratios

A Spectral Hilton--Milner--Frankl Theorem for $t$ -Intersecting Families

An improved range for the maximum critically $t$ -intersecting hypergraphs

Thresholds for the Frankl-Wang $3/7$ conjecture on maximum-degree ratios