On the number of hyperedges in the hypergraph of lines and pseudo-discs (Q2161213)

Summary: Consider a hypergraph whose vertex set is a family of \(n\) lines in general position in the plane, and whose hyperedges are induced by intersections with a family of pseudo-discs. We prove that the number of \(t\)-hyperedges is bounded by \(O_t(n^2)\) and that the total number of hyperedges is bounded by \(O(n^3)\). Both bounds are tight.