Tian Yao

activity

20242026

collaborators

8 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

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 $I ¨ _{t} (F)$ of $F$ as the minimum size of a subset $S$ of $[…

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

$s$ -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.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…

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

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

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

s-almost t-intersecting families for finite sets

Cross-intersection theorems for uniform partitions of finite sets

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

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

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

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