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.
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2-transitive A-code adjacency matrix algebra angles arccos association scheme automorphism group block design bound C-matrices columns combinatorial complement congruence order contains corresponding defined DEFINITION Delsarte denote dimension distance eigenvalues Eindhoven elements elliptic geometry equals equiangular lines equivalent Euclidean Example exists finite following theorem Golay code Gram matrix Gramian matrix graph of order Hadamard matrix Hence Higman implies Indag inner products integer J. J. Seidel J. M. Goethals Latin square lattice Lemma line graph linear Math matrix of order multiplicity n-subspaces non-adjacent obtained orthogonal pair parameters permutation groups Petersen graph polytopes Proc Proof proved rank regular two-graph Remark root systems satisfies Section set of lines smallest eigenvalue spanned spherical Steiner system strong graph strongly regular graphs subgraph subset subspace switching class symplectic t-design ternary Golay code Theorem 4.2 theory triples two-distance set unique unit vectors valency vector space vertices yields