Intersecting Families in a Subset of Boolean Lattices
Intersecting Families in a Subset of Boolean Lattices
Let $n, r$ and $\ell$ be distinct positive integers with $r < \ell\leq n/2$, and let $X_1$ and $X_2$ be two disjoint sets with the same size $n$. Define $$\mathcal{F}=\left\{A\in \binom{X}{r+\ell}: \mbox{$|A\cap X_1|=r$ or $\ell$}\right\},$$ where $X=X_1\cup X_2$. In this paper, we prove that if $\mathcal{S}$ is an intersecting family …