2014/03/31 by G. Greaves, Gary R. W. Greaves, J. H. Koolen +5 · 3 citations
Computer Science · Mathematics · #Combinatorics #Digital Image Processing Techniques #Discrete mathematics #Eigenvalues and eigenvectors #Equiangular polygon #Euclidean distance #Euclidean geometry #Euclidean space #Geometry #Graph theory and applications #Line (geometry) #Mathematical analysis #Mathematics #Physics #Point processes and geometric inequalities #Upper and lower bounds #math.CO #math.MG #msc:05B20 #msc:05B40
paper · pdf · doi:10.1016/j.jcta.2015.09.008
published as J. Combin. Theory Ser. A 138 (2016), pp. 208--235 · 24 pages, to appear in JCTA. Corrected an entry in Table 2
arxiv created 2015/09/22 · openalex publication_date 2015/11/11 · arxiv updated 2016/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We obtain several new results contributing to the theory of real equiangular line systems. Among other things, we present a new general lower bound on the maximum number of equiangular lines in d dimensional Euclidean space; we describe the two-graphs on 12 vertices; and we investigate Seidel matrices with exactly three distinct eigenvalues. As a result, we improve on two long-standing upper bounds regarding the maximum number of equiangular lines in dimensions d=14, and d=16. Additionally, we prove the nonexistence of certain regular graphs with four eigenvalues, and correct some tables from the literature.