On a Loomis-Whitney Type Inequality for Permutationally Invariant Unconditional Convex Bodies
Abstract
For a permutationally invariant unconditional convex body K in Rn we define a finite sequence (Kj), j = 1, ..., n of projections of the body K to the space spanned by first j vectors of the standard basis of Rn. We prove that the sequence of volumes (|K1|, ..., |Kn|) is log-concave.
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