10 papers
Forcing Quasirandomness via Rooted F-Densities
Heng Li, Xizhi Liu
Let be a finite graph with at least one edge, and let be a graphon. We show that if the density of rooted at each edge is almost everywhere constant, then either $t(F,W…
Intervals of uniform Turán densities
Heng Li, Xizhi Liu, Oleg Pikhurko
We prove that the set of uniform Turán densities of possibly infinite families of -graphs contains a terminal interval: there exists such that $[1-…
Nearly Sharp Bounds for Lattice Coverings by Convex Bodies
Heng Li, Xizhi Liu
The paper establishes a near‑linear upper bound on the lattice covering density of any n‑dimensional convex body, showing it is at most C·n log n (log log n)^{10/3+o(1)} and improv…
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…
Strong counterexamples to Mubayi's supersaturation conjecture in every uniformity
Heng Li, Hong Liu, Xizhi Liu +1
The supersaturation problem asks, for a fixed -graph , for the minimum number of copies of in an -vertex -graph with $\ex(n,\mathcal F)+q$ edges.…
On Mubayi's Polynomial-Ideal Conjecture and a Hypergraph Turán Theorem
Heng Li, Xizhi Liu
Among the many proofs of Turán's classical theorem, one particularly surprising proof due to Li and Li uses ideals in polynomial rings to record missing edges. Motivated by their…