Equiangular lines in Euclidean spaces

Abstract

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.

24 pages, to appear in JCTA. Corrected an entry in Table 2

References in corpus (5)

• Biregular graphs with three eigenvalues
• Concrete Constructions of Real Equiangular Line Sets
• Steiner equiangular tight frames
• Nonexistence of tight spherical design of harmonic index 4
• On eigenvalues of Seidel matrices and Haemers' conjecture

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• Symmetric and skew-symmetric $\{0,\pm 1\}$-matrices with large determinants
• Quantum Theory as Symmetry Broken by Vitality
• Optimal Parameter Configurations for Sequential Optimization of Variational Quantum Eigensolver
• Open problems in the spectral theory of signed graphs
• Real equiangular lines in dimension 18 and the Jacobi identity for complementary subgraphs
• Studies of symmetries that give special quantum states the "right to exist"
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• Surveying points in the complex projective plane
• Maximal Orthoplectic Fusion Frames from Mutually Unbiased Bases and Block Designs
• The Lemmens-Seidel conjecture and forbidden subgraphs
• Bounds for spherical codes
• Constructions of complex equiangular lines from mutually unbiased bases
• p-adic Welch Bounds and p-adic Zauner Conjecture
• On a question of Haemers regarding vectors in the nullspace of Seidel matrices
• Some Remarks on Systems of Equiangular Lines
• Maximal Sets of Equiangular Lines
• Sets of equiangular lines in dimension $18$ constructed from $A_9\oplus A_9\oplus A_1$