Author

Mei Lu

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Preprint Sep 2026

Counting $t$-wise $L$-intersecting cliques with prescribed intersection sizes

Let $r,t\ge 3$ be integers and $L=\{\ell_1,\ell_2,\ldots,\ell_s\}\subseteq [0,r-1]$ a fixed set of integers with $|L|\neq r$ and $\ell_1<\ell_2<\cdots<\ell_s$. For each integer $n$, let $\Psi_{r}(n,L,t)$ be the maximum number of $r$-cliques in an $n$-vertex graph whose $r$-cliques, viewed as a family of $r$-subsets of...

Yi-Yang Zhan, Yi-Chen Wang, Mei Lu · 0 citations

Preprint Sep 2026

The second-order term for the largest $r$-fork-free families

A family of subsets of $[n]$ is $r$-fork-free if none of its members is strictly contained in $r$ other distinct members. For each fixed integer $r\ge2$, we prove that the maximum size of such a family is \[ \binom{n}{\lfloor n/2\rfloor} \left(1+\frac{2(r-1)}{n}+o(n^{-1})\right). \] This determines the second-order ter...

Yi-Yang Zhan, Mei Lu, Xia-Miao Zhao · 1 citation