More Turán-type theorems for triangles in convex point sets (Q668054)

Summary: We study the following family of problems: Given a set of \(n\) points in convex position, what is the maximum number triangles one can create having these points as vertices while avoiding certain sets of \textit{forbidden configurations}. As forbidden configurations we consider all 8 ways in which a pair of triangles in such a point set can interact. This leads to 256 extremal Turán-type questions. We give nearly tight (within a \(\log n\) factor) bounds for 248 of these questions and show that the remaining 8 questions are all asymptotically equivalent to Stein's longstanding tripod packing problem.