Abstract

The lattice diameter, ℓ(P), of a convex polygon P in R 2 measures the longest string of integer points on a line contained in P. We relate the lattice diameter to the area and to the lattice width of P, w l(P) . We show, e.g., that w l⩽ 4 3 ℓ+1 , thus giving a discrete analogue of Blaschke's theorem.

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