8 papers
A complete solution to the Tokushige measure conjecture and its stability
Yongjiang Wu, Lihua Feng
We resolve three conjectures proposed by Tokushige in 2013 about cross -intersecting families of subsets and integer sequences. For and , def…
A Spectral Hilton--Milner--Frankl Theorem for -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 , the complete -star uniquely maximizes the adjacency-tensor spectra…
On a conjecture regarding the product version of the Hilton-Milner theorem
Xucheng Bu, Lihua Feng, Zejun Huang +2
Recently, Frankl and Wang considered a product version of the classical Hilton-Milner theorem. They conjectured that, if and $\mathcal{G} \subs…
Improved bound on symmetric differences of intersecting families
Lihua Feng, Zejun Huang, Qifan Wang +1
For a family , it is called intersecting if for all . We use $\mathcal{SD}(\mathcal{F}) = \{F \triangle G : F, G \in \math…
The Suda-Tanaka-Tokushige conjecture for -biased intersecting families
Yongjiang Wu, Lihua Feng
In 2017, Suda, Tanaka and Tokushige conjectured that if with , then every intersecting family satisfies…
Proof of Frankl's conjecture on cross-intersecting families
Yongjiang Wu, Lihua Feng, Yongtao Li
Two families and are called cross-intersecting if for every and , the intersection is non-empty. For any…
-intersecting or Configuration Forbidden Families on Set Systems and Vector Spaces over Finite Fields
Jiuqiang Liu, Guihai Yu, Lihua Feng +1
In this paper, we derive a tight upper bound for the size of an intersecting -Sperner family of subspaces of the -dimensional vector space over finite fi…
Snevily's Conjecture about -intersecting Families on Set Systems and its Analogue on Vector Spaces
Jiuqiang Liu, Guihai Yu, Lihua Feng +1
The classical Erdős-Ko-Rado theorem on the size of an intersecting family of -subsets of the set is one of the fundamental intersection theorems for s…