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Lattice coverings and the diagonal group
Published online by Cambridge University Press: 17 April 2009
Abstract
Let M be any bounded set in n-dimensional Euclidean space. Then almost all n-dimensional lattices L with determinant 1 have the following property: There exists a diagonal transformation D with determinant 1 (depending on L) such that L does not cover space with DM. Moreover, if M has non-empty interior, the exceptional (null-) set contains at least enumerably many diagonally non-equivalent lattices.
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- Copyright © Australian Mathematical Society 1987
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