Abstract
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.
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