Geometry and Combinatorics

Geometry and Combinatorics

1st Edition - May 7, 1991

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  • Author: J. J. Seidel
  • eBook ISBN: 9781483268002

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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.

Table of Contents

  • Preface


    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

Product details

  • No. of pages: 430
  • Language: English
  • Copyright: © Academic Press 1991
  • Published: May 7, 1991
  • Imprint: Academic Press
  • eBook ISBN: 9781483268002

About the Author

J. J. Seidel

About the Editors

D. G. Corneil

R. Mathon

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