Authors: Jojić, Duško
Vrećica, Siniša
Živaljević, Rade 
Title: Symmetric multiple chessboard complexes and a new theorem of Tverberg type
Journal: Journal of Algebraic Combinatorics
Volume: 46
Issue: 1
First page: 15
Last page: 31
Issue Date: 1-Aug-2017
Rank: M21
ISSN: 0925-9899
DOI: 10.1007/s10801-017-0743-9
Abstract: 
We prove a new theorem of Tverberg–van Kampen–Flores type, which confirms a conjecture of Blagojević et al. about the existence of ‘balanced Tverberg partitions’ (Conjecture 6.6 in [Tverberg plus constraints, Bull. London Math. Soc. 46:953–967 (2014]). The conditions in this theorem are somewhat weaker than in the original conjecture, and we show that the theorem is optimal in the sense that the new (weakened) condition is also necessary. Among the consequences is a positive answer (Theorem 7.2) to the ‘balanced case’ of the question asking whether each admissibler-tuple is Tverberg prescribable (Blagojević et al. 2014, Question 6.9).
Keywords: Chessboard complexes | Shellability | Simplicial complexes | Symmetrized deleted joins | Tverberg theorem | Van Kampen–Flores theorem
Publisher: Springer Link
Project: Topology, geometry and global analysis on manifolds and discrete structures 

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