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A Spectral Hilton--Milner--Frankl Theorem for -Intersecting Families
Xucheng Bu, Lihua Feng, Lihua Deng +2
Keevash, Lenz, and Mubayi proved a spectral Erdős--Ko--Rado theorem, showing that, for sufficiently large , the complete -star uniquely maximizes the adjacency-tensor spectra…
An improved range for the maximum critically -intersecting hypergraphs
Lu Lu, Rongrong Lu, Qifan Wang +1
The paper proves that for k-uniform hypergraphs that are t‑intersecting and t‑critical, the maximum number of edges is bounded by \(\binom{k+d}{d}\) when k > 30·d², confirming Fran…
The Second Largest Eigenvalue of Stiffness Matrices of Normalized Complete Frameworks
Tingting Wang, Lu Lu
Let be the normalized rigidity matrix of a framework in , and let \[ L(G,p)=R(G,p)R(G,p)^{T} \] be the associated stiffness matrix. We study the extre…
Thresholds for the Frankl-Wang conjecture on maximum-degree ratios
Zejun Huang, Zhiyi Liu, Lu Lu +1
Let be an intersecting family, , and $\varrho(\mathcal{F})=Î(\mathcal{F})/|\mathcal{…