Multiple chessboard complexes and the colored Tverberg problem

Following Karaguezian, Reiner and Wachs we study the connectivity degree and shellability of multiple chessboard complexes. Our central new results provide sharp connectivity bounds relevant to applications in Tverberg type problems where multiple points of the same color are permitted. The results presented in this paper also serve as a foundation for the new results of Tverberg–van Kampen–Flores type, as described in the sequel to this paper.