Abstract
The aim of this chapter is to give a characterization of extreme lattices, those lattices on which the Hermite invariant attains a local maximum. To this end, we introduce in Section 3.2 the two notions of perfection and eutaxy, and prove in Section 3.4 that they characterize extreme lattices; in particular, we obtain an algorithm which allows us to decide whether a given lattice is extreme, whose justification relies on the technical material in Sections 3.1 and 3.3. Then we give in Sections 3.5 and 3.6 a detailed analysis of the properties of perfection and eutaxy.
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© 2003 Springer-Verlag Berlin Heidelberg
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Martinet, J. (2003). Perfection and Eutaxy. In: Perfect Lattices in Euclidean Spaces. Grundlehren der mathematischen Wissenschaften, vol 327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05167-2_3
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DOI: https://doi.org/10.1007/978-3-662-05167-2_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07921-4
Online ISBN: 978-3-662-05167-2
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