Abstract
We suggest a method for selecting an L-simplex in an L-polyhedron of an n-lattice in Euclidean space. By taking into account the specific form of the condition that a simplex in the lattice is an L-simplex and by considering a simplex selected from an L-polyhedron, we present a new method for describing all types of L-polyhedra in lattices of given dimension n. We apply the method to deduce all types of L-polyhedra in n-dimensional lattices for n=2,3,4, which are already known from previous results.
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References
B. N. Delone, “The geometry of positive quadratic forms,” Uspekhi Mat. Nauk [Russian Math. Surveys], No. 4, 102-164 (1938).
R. M. Erdahl and S. S. Ryshkov, “The empty sphere,” Canad. J. Math., 39, No. 4, 794-824 (1987).
E. P. Baranovskii, E. V. Vlasov, and N. V. Novikova, “The structure of L-partitions of 4-lattices,” in: Dep. VINITI No. 78-B91 [in Russian], VINITI, Moscow (1991), pp. 1-38.
E. P. Baranovskii and P. G. Kononenko, “Two-sliced L-polyhedra of 5-lattices,” in: Dep. VINITI No. 387-B98 [in Russian], VINITI, Moscow (1998), pp. 1-28.
E. P. Baranovskii, “Simplexes of L-partitions of Euclidean spaces,” Mat. Zametki [Math. Notes], 10, No. 6, 659-670 (1971).
S. S. Ryshkov and R. M. Érdahl, “Slice construction of L-topes of lattices,” Uspekhi Mat. Nauk [Russian Math. Surveys], 44, No. 2, 241-242 (1989).
S. S. Ryshkov and E. P. Baranovskii, “C-types of η-lattices and 5-dimensional primitive parallelohedra (with applicationsto the theory of covers),” Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.], 137, 3-131 (1976).
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Baranovskii, E.P., Kononenko, P.G. A Method of Deducing L-Polyhedra for n-Lattices. Mathematical Notes 68, 704–712 (2000). https://doi.org/10.1023/A:1026648330397
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DOI: https://doi.org/10.1023/A:1026648330397