Abstract
LetK1,…Kn be convex sets inRd. For 0≦i =0, then {fx161-1} This inequality was conjectured by Katchalski and Perles. Equality holds, e.g., ifK1=…=Kr=Rd andKr+1,…,Kn aren−r hyperplanes in general position inRd. The proof uses multilinear techniques (exterior algebra). Applications to convexity and to extremal set theory are given.
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