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Finite coverings by translates of centrally symmetric convex domains

1987; Springer Science+Business Media; Volume: 2; Issue: 4 Linguagem: Inglês

10.1007/bf02187889

1432-0444

Gézá Tóth,

Rings, Modules, and Algebras

Bambah and Rogers proved that the area of a convex domain in the plane which can be covered byn translates of a given centrally symmetric convex domainC is at most (n−1)h(C)+a(C), whereh(C) denotes the area of the largest hexagon contained inC anda(C) stands for the area ofC. An improvement with a term of magnitude √n is given here. Our estimate implies that ifC is not a parallelogram, then any covering of any convex domain by at least 26 translates ofC is less economic than the thinnest covering of the whole plane by translates ofC.