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Low dimensional lattices have a strict Voronoï basis
Author(s) -
Mayer Andrew J.
Publication year - 1995
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300014558
Subject(s) - mathematics , minkowski space , basis (linear algebra) , generalization , dimension (graph theory) , lattice (music) , pure mathematics , mathematical analysis , geometry , physics , acoustics
We prove a generalization of a theorem of Ryshkov relating the Voronoï vectors of lattices to the defining conditions for the Minkowski fundamental domainM n . This is then used to prove that a Minkowski reduced basis of a lattice of dimension n < 7 consists of strict Voronoï vectors.