Premium
A lattice without a basis of minimal vectors
Author(s) -
Conway J. H.,
Sloane N. J. A.
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/s002557930001144x
Subject(s) - mathematics , lattice (music) , basis (linear algebra) , combinatorics , pure mathematics , geometry , physics , acoustics
It is shown that in all dimensions n ≥ 11 there exists a lattice which is generated by its minimal vectors but in which no set of n minimal vectors forms a basis.