In pursuit of colored Carathéodory-Bárány theorems

Rade Zivaljevi\'c

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, [2], [6], [15], [20] and more recent results related to the Tverberg--Vre\'cica conjecture, [17], [18].

Keywords: Combinatorial geometry, Carathéodory theorem, Tverberg theorem

Classification (MSC2000): 52A20; 52A35, 55N91

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