Abstract
In this paper we give a complete geometrical theory for the study of the exact lower bound of the density of n-dimensional lattices. For arbitrary (r, R)-systems we prove an analog of well known theorems due to Rogers from the theory of packings, and also from this same theory, an analog of a theorem due to Coxeter, Few, and Rogers. Several special examples are treated.
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Translated from Matematicheskie Zametki, Vol. 16, No. 3, pp. 447–454, September, 1974.
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Ryshkov, S.S. Density of an (r, R)-system. Mathematical Notes of the Academy of Sciences of the USSR 16, 855–858 (1974). https://doi.org/10.1007/BF01148135
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DOI: https://doi.org/10.1007/BF01148135