The Conway-Sloane tetralattice pairs are non-isometric

2009/10/12 by Juan Marcos Cerviño, Juan Marcos Cervino, Cervino, Juan Marcos +2
Chemistry · Mathematics · #11E45 #11F11 #11F27 #Advanced Combinatorial Mathematics #Chemistry and Stereochemistry Studies #FOS: Mathematics #Number Theory (math.NT) #Organometallic Compounds Synthesis and Characterization #math.NT #msc:11E45 #msc:11F11 #msc:11F27

paper · pdf · doi:10.48550/arxiv.0910.2127

10 pages

arxiv created 2009/10/12 · openalex publication_date 2009/10/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 different, and verified 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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