This volume brings together selected works of professor J.J. Seidel, one of the most influential contemporary mathematicians. His ideas on elliptic geometry, codes, distance sets and strongly regular graphs have had an enormous impact on the mathematical community. For the first time his papers, many of which are scattered throughout obscure conference proceedings, are gathered in this single volume. The volume has four sections - graphs and designs, lines with few angles, matrices and forms and non-euclidean geometry. Professor Seidel has written introductions to each of these sections, placing the work in context and indicating new lines of research.
Part 1 Graphs and design: equilateral point sets in elliptic geometry.
Strongly regular graphs of L2-type and of triangular type; strongly regular
graphs with (-1,1,0) adjacency matrix having eigenvalue 3, J.H.van Lint;
strongly regular graphs derived from combinatorial designs, J.M.Goethals; a
strongly regular graph derived from the perfect ternary golay code,
E.R.Berlekamp and J.H.van Lint; spherical codes and design, P.Delsarte and
J.M.Goethals; graphs related to exceptional root systems, F.C.Bussemaker and
D.M.Cvetkovic; strongly regular graphs having strongly regular
subconstituents, P.J.Cameron and J.M.Goethals. Part 2 Lines with few angles:
equiangular lines. A survey of two-graphs, P.W.H.Lemmens; the regular
two-graph on 276 vertices, J.M.Goethals; bounds for systems of lines, and
jacobi polynomials, P.Delsarte and J.M.Goethals; line graphs, root systems,
and elliptic geometry, P.J.Cameron et al; two graphs - a second survey,
D.E.Taylor. Part 3 Matrices and Forms: orthogonal matrices with zero
diagonal. Quasiregular two-distance sets, J.M.Goethals; a skew Hadamard
matrix of order 36, J.M.Goethals; symmetric Hadamard matrices of order 36,
F.C.Bussemaker; quadratic forms over GF(2). On two-graphs and Shult's
characterization of symplectic and orthogonal geometries over GF(2),
P.J.Cameron; the Krein condition, spherical designs, Norton algebras, and
permutation groups, P.J.Cameron and J.M.Goethals. Part 4 Non-euclidean
geometry: the congruence order of the elliptic plane, J.Haantjes;
equi-isoclinic subspaces of Euclidean spaces. Metric problems in elliptic
geometry, P.W.H.Lemmens; the football, J.M.Goethals; discrete hyperbolic
geometry, A.Neumaier; few distance sets in Rpq, A.Blokhuis; remark on
Wielandt's visibility theorem, A.Blokhuis.
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