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Journal of the London Mathematical Society 1992 s2-45(2):193-200; doi:10.1112/jlms/s2-45.2.193
© 1992 by London Mathematical Society
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© Oxford University Press

Thin Lattice Coverings

J. A. Rush

Department of Mathematics, University of Edinburgh Edinburgh EH9 3JZ

Let G be a compact body of positive volume in Rn, star-shaped with respect to an interior point, taken to be the origin. For subsets ohm of Rn, the functional


Formula

represents the minimum density with which ohm can be covered by a lattice {wedge} of translates of G. We obtain an upper bound on IL(G, Zn).

If the attributes of G are supplemented with convexity, write H instead. We also bound above


Formula

the classical minimum lattice-covering density of H. No symmetry conditions are imposed on G and H.

Present address: Department of Mathematics, GN-50 University of Washington, Seattle, Washington 98195, USA


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