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The Conway-Sloane tetralattice pairs are non-isometric

Juan Cervino and Georg Hein

Number 35
Authors Juan Cervino
Georg Hein
Year 2009

Conway and Sloane constructed a 4-parameter family of pairs of isospectral lattices of rank four. They conjectured that all pairs in their family are non-isometric, whenever the parameters are pairwise di erent, and veri ed this for classical integral lattices of determinant up to 104. In this paper, we use our theory of lattice invariants to prove this conjecture.

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