Geometry and Combinatorics

Geometry and Combinatorics: Selected Works of J. J. Seidel brings together some of the works of J. J. Seidel in geometry and combinatorics. Seidel's selected papers are divided into four areas: graphs and designs; lines with few angles; matrices and forms; and non-Euclidean geometry. A list of all of Seidel's publications is included. Comprised of 29 chapters, this book begins with a discussion on equilateral point sets in elliptic geometry, followed by an analysis of strongly regular graphs of L2-type and of triangular type. The reader is then introduced to strongly regular graphs with (-1, 1, 0) adjacency matrix having eigenvalue 3; graphs related to exceptional root systems; and equiangular lines. Subsequent chapters deal with the regular two-graph on 276 vertices; the congruence order of the elliptic plane; equi-isoclinic subspaces of Euclidean spaces; and Wielandt's visibility theorem. This monograph will be of interest to students and practitioners in the field of mathematics.

Preface

Acknowledgments

List of Publications

I. Graphs and Designs

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

Strongly Regular Graphs Derived from Combinatorial Designs

A Strongly Regular Graph Derived from the Perfect Ternary Golay Code

Spherical Codes and Designs

Graphs Related to Exceptional Root Systems

Strongly Regular Graphs Having Strongly Regular Subconstituents

II. Lines with Few Angles

Equiangular Lines

A Survey of Two-Graphs

The Regular Two-Graph on 276 Vertices

Bounds for Systems of Lines, and Jacobi Polynomials

Line Graphs, Root Systems, and Elliptic Geometry

Two-Graphs, a Second Survey

III. Matrices and Forms

Orthogonal Matrices with Zero Diagonal

Quasiregular Two-Distance Sets

A Skew Hadamard Matrix of Order 36

Symmetric Hadamard Matrices of Order 36

Quadratic Forms over GF(2)

On Two-Graphs and Shult's Characterization of Symplectic and Orthogonal Geometries Over GF(2)

The Krein Condition, Spherical Designs, Norton Algebras and Permutation Groups

IV. Non-Euclidean Geometry

The Congruence Order of the Elliptic Plane

Equi-Isoclinic Subspaces of Euclidean Spaces

Metric Problems in Elliptic Geometry

The Football

Discrete Hyperbolic Geometry

Few Distance Sets in Rp,q

Remark on Wielandt's Visibility Theorem

Complete List of Permissions