Dehai Liu

activity

20232026

collaborators

9 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

Non-trivial cross- $t$ -intersecting families for vector spaces with the maximum sum of sizes

Dehai Liu, Kaishun Wang, Tian Yao

Let $V$ be an $n$ -dimensional vector space over a finite field. Suppose that $F$ and $G$ are non-empty families of $k$ -subspaces and $ℓ$ -subspaces of $V$ , re…

math.CO2026

$s$ -almost cross- $t$ -intersecting families for vector spaces

Dehai Liu, Jinhua Wang, Tian Yao

Let $V$ be an $n$ -dimensional vector space over the finite field $F_{q}$ , and $[k V]$ denote the family of all $k$ -dimensional subspaces of $V$ . The families $\mat…

math.CO2026

Extremal $t$ -intersecting families for finite sets with $t$ -covering number at least $t + 2$

Tian Yao, Dehai Liu, Kaishun Wang

Let $F \subseteq (k [ n ])$ be a $t$ -intersecting family. Define the $t$ -covering number $τ_{t} (F)$ of $F$ as the minimum size of a subset $S$ of $[n…

math.CO2025

$s$ -almost cross- $t$ -intersecting families for finite sets

Dehai Liu, Kaishun Wang, Tian Yao

Two families $F$ and $G$ of $k$ -subsets of an $n$ -set are called $s$ -almost cross- $t$ -intersecting if each member in $F$ (resp. $G$ ) is $t$ -…

math.CO2024

$s$ -almost $t$ -intersecting families for finite sets

Dehai Liu, Kaishun Wang, Tian Yao

A family $F$ of $k$ -subsets of an $n$ -set is called $s$ -almost $t$ -intersecting if each member is $t$ -disjoint with at most $s$ members. In this paper, we prove that, if…

math.CO2024

$s$ -almost $t$ -intersecting families for vector spaces

Lijun Ji, Dehai Liu, Kaishun Wang +2

Let $V$ be a finite dimensional vector space over a finite field, and $F$ a family consisting of $k$ -subspaces of $V$ . The family $F$ is called $t$ -intersecting…

math.CO2024

The maximum sum of sizes of non-empty cross $t$ -intersecting families

Shuang Li, Dehai Liu, Deping Song +1

Let $[n] := {1, 2, \dots, n}$ , and $M$ be a set of positive integers. Denote the family of all subsets of $[n]$ with sizes in $M$ by $(M [ n ])$ . The non-…

math.CO2023

More on $r$ -cross $t$ -intersecting families for vector spaces

Tian Yao, Dehai Liu, Kaishun Wang

Let $V$ be a finite dimensional vector space over a finite field. Suppose that $F_{1}$ , $F_{2}$ , $\dots$ , $F_{r}$ are $r$ -cross $t$ -intersecting families of…

The complete nontrivial-intersection theorem for vector spaces

Non-trivial cross-t-intersecting families for vector spaces with the maximum sum of sizes

s-almost cross-t-intersecting families for vector spaces

Extremal t-intersecting families for finite sets with t-covering number at least t+2

s-almost cross-t-intersecting families for finite sets

s-almost t-intersecting families for finite sets

s-almost t-intersecting families for vector spaces

The maximum sum of sizes of non-empty cross t-intersecting families

More on r-cross t-intersecting families for vector spaces

Non-trivial cross- $t$ -intersecting families for vector spaces with the maximum sum of sizes

$s$ -almost cross- $t$ -intersecting families for vector spaces

Extremal $t$ -intersecting families for finite sets with $t$ -covering number at least $t + 2$

$s$ -almost cross- $t$ -intersecting families for finite sets

$s$ -almost $t$ -intersecting families for finite sets

$s$ -almost $t$ -intersecting families for vector spaces

The maximum sum of sizes of non-empty cross $t$ -intersecting families

More on $r$ -cross $t$ -intersecting families for vector spaces