2016
DOI: 10.1090/noti1415
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Tverberg's Theorem at 50: Extensions and Counterexamples

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Cited by 35 publications
(29 citation statements)
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“…The purpose of this survey is to give a broad overview of the current state of the field and point out key open problems. Other surveys covering different aspects of Tverberg's theorem can be found in [Eck79,Eck93,Mat02,BBZ16,DLGMM17,BZ17].…”
Section: Introductionmentioning
confidence: 99%
“…The purpose of this survey is to give a broad overview of the current state of the field and point out key open problems. Other surveys covering different aspects of Tverberg's theorem can be found in [Eck79,Eck93,Mat02,BBZ16,DLGMM17,BZ17].…”
Section: Introductionmentioning
confidence: 99%
“…, X r such that conv X 1 ∩ · · · ∩ conv X r = ∅, and this number of points is optimal in general [19]. Since then a multitude of extensions and variants of this result have been proven; see for instance the recent survey article [2].…”
Section: Introductionmentioning
confidence: 89%
“…Recently in [124] the authors showed that the Tverberg number in Z 2 is exactly 4r − 3 when r ≥ 3 and improved the upper bounds for the Tverberg numbers of Z 3 . [42] and, for the two-dimensional case, [341].…”
Section: Tverbergmentioning
confidence: 99%
“…The current state of affairs is that a counter-example is known for every r that is not a prime power and for every d ≥ 2r. See the survey [42] for more details.…”
Section: Tverbergmentioning
confidence: 99%