Author

P. Frankl

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Preprint Oct 2026

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

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 product on disjoint sets attains this maximum whenever $p,q\ge2$ and $n\ge2^{15}(p+q-2)^3$. Together with the second author's result for $p=...

Fan-Qiang-Zou-Fei Chang, P. Frankl, Jian Wang · 0 citations

Preprint Aug 2026

Stability for Helly-type and triangle-free families

We consider $k$-graphs, $\mathcal{F}\subset \binom{[n]}{k}$, $k\geq 3$. A $k$-graph is called intersecting if any two of its edges have non-empty intersection. It is called a star if all its edges share a common vertex. The $k$-graph $\mathcal{F}$ is called Helly if all its intersecting subfamilies are stars. If the sa...

P. Frankl, Jian Wang · 0 citations