Several generalizations of Tverberg’s theorem

@article{Reay1979SeveralGO,
  title={Several generalizations of Tverberg’s theorem},
  author={John R. Reay},
  journal={Israel Journal of Mathematics},
  year={1979},
  volume={34},
  pages={238-244}
}
AbstractIn a generalization of Radon’s theorem, Tverberg showed that each setS of at least (d+1) (r − 1)+1 points inRdhas anr-partition into (pair wise disjoint) subsetsS =S1 ∪ … ∪Srso that $$\bigcap\nolimits_i^r {\underline{\underline {}} } _1 $$ convSi# Ø. This note considers the following more general problems: (1) How large mustS σRdbe to assure thatS has anr-partitionS=S1∪ … ∪Srso that eachn members of the family {convSi∼i-1r have non-empty intersection, where 1<=n<=r. (2) How large mustS… CONTINUE READING

Citations

Publications citing this paper.
SHOWING 1-5 OF 5 CITATIONS

The partition conjecture

  • Discrete Mathematics
  • 2000
VIEW 5 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

Regular Polygonal Partitions of a Tverberg Type.

Leah Leiner, Steven Simon
  • 2019
VIEW 3 EXCERPTS
CITES BACKGROUND

Helge Tverberg A celebration of a life in mathematics

  • Discrete Mathematics
  • 2001
VIEW 1 EXCERPT
CITES BACKGROUND