Benjian Lv

collaborators

7 papers

math.CO2026

The complete nontrivial-intersection theorem for vector spaces

Dehai Liu, Benjian Lv, Kaishun Wang +1

A family of $k$ -subspaces of an $n$ -dimensional vector space over a finite field is $t$ -intersecting if any two members intersect in a subspace of dimension at least $t$ . A $t$ -int…

math.CO2026

Sharp stability for cross $t$ -intersecting families of permutations in the linear range

Jie Wen, Benjian Lv

Two families $F, G \subseteq S_{n}$ are cross $t$ -intersecting if every $σ \in F$ and $τ \in G$ agree on at least $t$ points. A $t$ -coset is a coset…

math.CO2026

Structure of large $t$ -intersecting families I: Stability for the Hilton--Milner--Frankl theorem

Jie Wen, Benjian Lv

We study the structure of large $t$ -intersecting families. A family of $k$ -subsets of an $n$ -set is $t$ -intersecting if every two of its members intersect in at least $t$ elements.…

math.CO2026

On the Frankl--Tokushige conjecture and almost complete $r$ -cross $t$ -intersection theorems for vector spaces

Yao Li, Benjian Lv, Jie Wen

Let $r \geq 3$ and $k_{1} \geq k_{2} \geq \dots \geq k_{r} \geq t$ . Let $F_{1}, F_{2}, \dots, F_{r}$ be families of subspaces, of respective dimensions $k_1,k_2,\ldots,k_…

math.CO2026

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…

math.CO2026

On $r$ -cross $t$ -intersecting families of partitions

Jie Wen, Benjian Lv

In this paper, we address several intersection problems for $r$ -cross $t$ -intersecting families of partitions. A $k$ -partition of an $n$ -set $X$ is a set of $k$ pairwise disjoint n…

math.CO2025

Erdős-Ko-Rado theorem and Hilton-Milner type theorem for $k$ -partitions

Jie Wen, Benjian Lv

A $k$ -partition of an $n$ -set $X$ is a collection of $k$ pairwise disjoint non-empty subsets whose union is $X$ . A family of $k$ -partitions of $X$ is called $t$ -intersecting if any…

The complete nontrivial-intersection theorem for vector spaces

Sharp stability for cross t-intersecting families of permutations in the linear range

Structure of large t-intersecting families I: Stability for the Hilton--Milner--Frankl theorem

On the Frankl--Tokushige conjecture and almost complete r-cross t-intersection theorems for vector spaces

A unified approach to cross-intersection problems with applications to Hilton--Milner type theorems and stability

On r-cross t-intersecting families of partitions

Erdős-Ko-Rado theorem and Hilton-Milner type theorem for k-partitions

Sharp stability for cross $t$ -intersecting families of permutations in the linear range

Structure of large $t$ -intersecting families I: Stability for the Hilton--Milner--Frankl theorem

On the Frankl--Tokushige conjecture and almost complete $r$ -cross $t$ -intersection theorems for vector spaces

On $r$ -cross $t$ -intersecting families of partitions

Erdős-Ko-Rado theorem and Hilton-Milner type theorem for $k$ -partitions