Abstract
We study certain lattices constructed from finite abelian groups. We show that such a lattice is eutactic, thereby confirming a conjecture by Böttcher, Eisenbarth, Fukshansky, Garcia, Maharaj. Our methods also yield simpler proofs of two known results: First, such a lattice is strongly eutactic if and only if the abelian group has odd order or is elementary abelian. Second, such a lattice has a basis of minimal vectors, except for the cyclic group of order 4.
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This author supported by Deutsche Forschungsgemeinschaft (DFG), Project SCHU1503/7-1.
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Ladisch, F. Lattices of Finite Abelian Groups. Discrete Comput Geom 65, 938–951 (2021). https://doi.org/10.1007/s00454-019-00163-1
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DOI: https://doi.org/10.1007/s00454-019-00163-1