On an Analog to Minkowski’s Lattice Point Theorem

J. M. Wills
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J. M. Wills: University of Siegen, Dept. of Mathematics

A chapter in The Geometric Vein, 1981, pp 285-288 from Springer

Abstract: Abstract For a convex body K ⊂ E d let V(K) be its volume and G(K) = card(K ⋂ ℤ d ) [G 0(K) = card(int K ⋂ ℤ d )] be the lattice point number of K [int K]. If K is central symmetric (K = — K), then by Minkowski’s fundamental theorem 1 $$ {G^0}(K) = 1 \Rightarrow V(K) \leqslant {{\text{2}}^d}. $$

Keywords: Convex Hull; Lattice Point; Convex Body; Central Symmetry; Discrete Function (search for similar items in EconPapers)
Date: 1981
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-5648-9_20

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DOI: 10.1007/978-1-4612-5648-9_20

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