Classifying unavoidable Tverberg partitions

Boris Bukh, Po-Shen Loh, Gabriel Nivasch

Let $T(d,r)=(r-1)(d+1)+1$ be the parameter in Tverberg's theorem, and call a partition $\mathcal{I}$ of $\{1,2,\dots ,T(d,r)\}$ into $r$ parts a "Tverberg type". We say that $\mat…