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On Tverbergʼs theorem

✍ Scribed by Ricardo Strausz; Pablo Soberón


Book ID
119236651
Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
245 KB
Volume
38
Category
Article
ISSN
1571-0653

No coin nor oath required. For personal study only.


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Theorem 1. For any integers r, d>1 there exists an integer T=T(d, r), such that given sets A 1 , ..., A d+1 /R d in general position, consisting of T points each, one can find disjoint (d+1)-point sets S 1 , ..., S r such that each S i contains exactly one point of each A j , j=1, 2, ..., d+1, and t