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Given a finite family $\mathcal{F}$ of convex sets in ℝd , we say that $\mathcal{F}$ has the (p,q)r property if for any p convex sets in $\mathcal{F}$ there are at least r q-tuples that have nonempty intersection. The piercing number of $\mathcal{F}$ is the minimum number of points we need to intersect all the sets in $\mathcal{F}$. In this paper we will find some bounds for the piercing number of families of convex sets with (p,q)r properties.

Piercing Numbers for Balanced and Unbalanced Families