Jian Wang

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20242026

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4 papers · 1 filter

math.CO2026

Proving the optimality of the product construction for the intersection--union problem

Fan Chang, Peter Frankl, Jian Wang

Let $m (n, p, q)$ be the largest size of a family of subsets of $[n]$ whose members pairwise intersect in at least $p$ vertices and omit at least $q$ common vertices. We prove that a…

math.CO2026

Stability for Helly-type and triangle-free families

Peter Frankl, Jian Wang

We consider $k$ -graphs, $F \subset (k [ n ])$ , $k \geq 3$ . A $k$ -graph is called intersecting if any two of its edges have non-empty intersection. It is called a star…

math.CO2026

A product version of the Hilton-Milner Theorem II

Peter Frankl, Jian Wang

Two families $F, G$ of $k$ -subsets of ${1, 2, \dots, n}$ are called {\it non-trivial cross-intersecting} if $F \cap G \neq = \emptyset$ for all $F\in \mathcal{F}, G\…

math.CO2026

The exact Erdős-Ko-Rado Theorem for 3-wise $t$ -intersecting uniform families

Peter Frankl, Jian Wang

One of the central problems in extremal set theory is the determination of the maximum size of an $r$ -wise $t$ -intersecting $k$ -graph on $n$ vertices. For $r = 2$ after decades of ef…

Proving the optimality of the product construction for the intersection--union problem

Stability for Helly-type and triangle-free families

A product version of the Hilton-Milner Theorem II

The exact Erdős-Ko-Rado Theorem for 3-wise t-intersecting uniform families

The exact Erdős-Ko-Rado Theorem for 3-wise $t$ -intersecting uniform families