PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 57(71) (dedicated to Djuro Kurepa), pp. 91--100 (1995)
In pursuit of colored Carathéodory-Bárány theorems
Rade Zivaljevi\'cMatematicki institut SANU, Beograd, Yugoslavia
Abstract: One of the shortest and the most elegant proofs of the well known Tverberg theorem, due to Karanbir Sarkaria, relies on a generalization of Carathéodory's theorem found by Imre Bárány. Our objective is to set up the stage for studying other Carathéodory--Bárány type results which should open a possibility for similar proofs of related Tverberg type statements. Among the Tverberg type results which motivate this study are colored Tverberg theorems, , , ,  and more recent results related to the Tverberg--Vre\'cica conjecture, , .
Keywords: Combinatorial geometry, Carathéodory theorem, Tverberg theorem
Classification (MSC2000): 52A20; 52A35, 55N91
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