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- W2949152021 abstract "Every convex body K in R^n has a coordinate projection PK that contains at least vol(0.1 K) cells of the integer lattice PZ^n, provided this volume is at least one. Our proof of this counterpart of Minkowski's theorem is based on an extension of the combinatorial density theorem of Sauer, Shelah and Vapnik-Chervonenkis to Z^n. This leads to a new approach to sections of convex bodies. In particular, fundamental results of the asymptotic convex geometry such as the Volume Ratio Theorem and Milman's duality of the diameters admit natural versions for coordinate sections." @default.
- W2949152021 created "2019-06-27" @default.
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- W2949152021 date "2004-03-16" @default.
- W2949152021 modified "2023-09-27" @default.
- W2949152021 title "Integer cells in convex sets" @default.
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