8 papers
Upper-shadow comparisons on the slice and the Frankl--Tokushige product conjectures
Fan Chang, Hong Liu, Miao Liu
Let , and let be the family of all -sets containing a member of . Writing $μ_k(\mathcal{F})=|\…
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 at fixed edge density. We prove a higher-order version in which the prescribed quantity…
Tree suspensions and transfer functions for single degree Turán spectra
Jiangdong Ai, Laihao Ding, Hong Liu +1
For integers , let denote the single-forbidden -degree Turán spectrum of -uniform hypergraphs. We introduce transfer functions for this spectrum:…
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 pai…
Vanishing orders, suspensions and zero degree Turán densities
Jiangdong Ai, Laihao Ding, Hong Liu +1
For integers , the -degree Turán density measures the minimum -degree threshold that forces a copy of a fixed -uniform hypergraph , gen…
A sharp -biased product bound for -cross-intersecting families
Fan Chang, Hong Liu, Miao Liu
We prove a sharp product theorem for -cross-intersecting families in the -biased measure. If , , and $\mathcal{F}_1,\dots,\mathcal{F}_r\subset…