On Cross-Intersecting Uniform Sub-Families of Hereditary Families
On Cross-Intersecting Uniform Sub-Families of Hereditary Families
A family $\mathcal{H}$ of sets is hereditary if any subset of any set in $\mathcal{H}$ is in $\mathcal{H}$. If two families $\mathcal{A}$ and $\mathcal{B}$ are such that any set in $\mathcal{A}$ intersects any set in $\mathcal{B}$, then we say that $(\mathcal{A}, \mathcal{B})$ is a cross-intersection pair (cip). We say that …