7 papers
The complete nontrivial-intersection theorem for vector spaces
Dehai Liu, Benjian Lv, Kaishun Wang +1
A family of -subspaces of an -dimensional vector space over a finite field is -intersecting if any two members intersect in a subspace of dimension at least . A -int…
Sharp stability for cross -intersecting families of permutations in the linear range
Jie Wen, Benjian Lv
Two families are cross -intersecting if every and agree on at least points. A -coset is a coset…
Structure of large -intersecting families I: Stability for the Hilton--Milner--Frankl theorem
Jie Wen, Benjian Lv
We study the structure of large -intersecting families. A family of -subsets of an -set is -intersecting if every two of its members intersect in at least elements.…
On the Frankl--Tokushige conjecture and almost complete -cross -intersection theorems for vector spaces
Yao Li, Benjian Lv, Jie Wen
Let and . Let be families of subspaces, of respective dimensions $k_1,k_2,\ldots,k_…
A unified approach to cross-intersection problems with applications to Hilton--Milner type theorems and stability
Jie Wen, Benjian Lv
We develop a new approach to cross-intersection problems in extremal set theory. The method builds on the iterative procedure introduced by Kupavskii and Zakharov (2024) and the $t…
On -cross -intersecting families of partitions
Jie Wen, Benjian Lv
In this paper, we address several intersection problems for -cross -intersecting families of partitions. A -partition of an -set is a set of pairwise disjoint n…
Erdős-Ko-Rado theorem and Hilton-Milner type theorem for -partitions
Jie Wen, Benjian Lv
A -partition of an -set is a collection of pairwise disjoint non-empty subsets whose union is . A family of -partitions of is called -intersecting if any…