Tian Yao

activity

20202026

collaborators

15 papers

math.CO2026

On Erdős--Ko--Rado and Hilton--Milner Theorems for Direct Products

Tian Yao, Mengyu Cao, Kaishun Wang

We investigate $t$ -intersecting families in direct-product set systems obtained by prescribing the number of selected elements in each part of a partitioned ground set. For a finit…

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

Cross-intersection theorems for uniform partitions of finite sets

Tian Yao, Mengyu Cao, Haixiang Zhang

A set partition is $c$ -uniform if every block has size $c$ . Two families of $c$ -uniform partitions of a finite set are said to be cross $t$ -intersecting if two partitions from diff…

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…

math.CO2022

Cross $t$ -intersecting families for symplectic polar spaces

Tian Yao, Kaishun Wang

Let $P$ be a symplectic polar space over a finite field $F_{q}$ , and $P_{m}$ denote the collection of all $k$ -dimensional totally isotropic subspace in $\m…

math.CO2022

Cross $t$ -intersecting families for finite affine spaces

Tian Yao, Kaishun Wang

Denote the collection of all $k$ -flats in $A G (n, F_{q})$ by $M (k, n)$ . Let $F_{1} \subset M (k_{1}, n)$ and $F_{2} \subset M (k_{2}, n)$ sati…

math.CO2021

Large non-trivial $t$ -intersecting families for signed sets

Tian Yao, Benjian Lv, Kaishun Wang

For positive integers $n, r, k$ with $n \geq r$ and $k \geq 2$ , a set ${(x_{1}, y_{1}), (x_{2}, y_{2}), \dots, (x_{r}, y_{r})}$ is called a $k$ -signed $r$ -set on $[n]$ if $x_{1}, \dots, x_{r}$ are distinct ele…

math.CO2020

Non-trivial $t$ -intersecting families for symplectic polar spaces

Tian Yao, Benjian Lv, Kaishun Wang

Let $P$ be a symplectic polar space over a finite field $F_{q}$ , and $P_{m}$ denote the set of all $m$ -dimensional subspaces in $P$ . We say a $t$ …

math.CO2020

Extremal $t$ -intersecting families for direct products

Tian Yao, Benjian Lv, Kaishun Wang

In this paper, by shifting technique we study $t$ -intersecting families for direct products where the ground set is divided into several parts. Assuming the size of each part is su…

On Erdős--Ko--Rado and Hilton--Milner Theorems for Direct Products

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

Cross-intersection theorems for uniform partitions of finite sets

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

Cross t-intersecting families for symplectic polar spaces

Cross t-intersecting families for finite affine spaces

Large non-trivial t-intersecting families for signed sets

Non-trivial t-intersecting families for symplectic polar spaces

Extremal t-intersecting families for direct products

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

Cross $t$ -intersecting families for symplectic polar spaces

Cross $t$ -intersecting families for finite affine spaces

Large non-trivial $t$ -intersecting families for signed sets

Non-trivial $t$ -intersecting families for symplectic polar spaces

Extremal $t$ -intersecting families for direct products