7 papers · 1 filter
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 -uniform hypergraph is -cancellative if $(\cup_{i=1}^t A_i)\cup B\ne (\cup_{i=…
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})=|\…
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…
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…
Sharp asymptotic bounds for uniform union-free hypergraphs
Miao Liu, Chong Shangguan, Chenyang Zhang
An -uniform hypergraph is called -union-free if any two distinct subsets of at most edges have distinct union. The study of union-free hypergraphs has multiple origins an…
Asymptotically sharp bounds for cancellative and union-free hypergraphs
Miao Liu, Chong Shangguan, Chenyang Zhang
An -graph is called -cancellative if for arbitrary distinct edges , it holds that ; it is cal…
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…