3 problems

Let $P=P_0\cup\cdots\cup P_d\subset\mathbb{R}^d$ be partitioned into $d+1$ color classes, with the origin in the relative interior of every $\operatorname{conv}(P_i)$, and let colo…

Let $3n$ straight lines in general position be given in the plane, and partition them into three color classes of $n$ lines each. The dual colorful Tverberg theorem. The lines can…

The colorful Tverberg theorem concerns collections of colored points and partitions satisfying the colorful condition that each partition block contains one point of each color, wi…