Multiple chessboard complexes and the colored Tverberg problem
Combinatorics
2015-10-20 v3
Abstract
Following D.B. Karaguezian, V. Reiner, and M.L. Wachs (Matching Complexes, Bounded Degree Graph Complexes, and Weight Spaces of -Complexes, Journal of Algebra 2001) we study the connectivity degree and shellability of multiple chessboard complexes. Our central new results (Theorems 3.2 and 4.4) provide sharp connectivity bounds relevant to applications in Tverberg type problems where multiple points of the same color are permitted. These results also provide a foundation for the new results of Tverberg-van Kampen-Flores type, as announced in arXiv:1502.05290 [math.CO].
Keywords
Cite
@article{arxiv.1412.0386,
title = {Multiple chessboard complexes and the colored Tverberg problem},
author = {Duško Jojić and Siniša T. Vrećica and Rade T. Živaljević},
journal= {arXiv preprint arXiv:1412.0386},
year = {2015}
}
Comments
Exposition is substantially improved