Geometry and combinatorics. Selected works of J. J. Seidel. Ed. by D. G. Corneil and R. Mathon.

*(English)*Zbl 0770.05001
Boston, MA: Academic Press. xix, 410 p. (1991).

The authors have selected 28 papers out of the 114 written by J. J. Seidel in the period 1947-1990. Since Seidel devoted the first 20 years of his career to education and the creation of the mathematics department at Eindhoven University of Technology, 100 of these papers were actually written in the last 25 years of that period. The reprinted papers have been grouped into four sections of roughly the same size but there are strong connections between these sections.

Section 1, Graphs and designs, starts with a paper written jointly with the reviewer. This started Seidel’s impressive contributions to the theory of strongly regular graphs and to spherical codes and designs. A proof that Seidel is one of those mathematicians who are at their best when collaborating with others is provided by the fact that 22 of the papers in this book were written with one or more authors. Of these, J.- M. Goethals, Ph. Delsarte, and P. J. Cameron had the strongest influence on his work. In fact 10 of the 14 papers with Goethals occur in these selected works.

Section 2, Lines with few angles, contains work related to two-graphs, including the two important surveys on the subject.

Section 3, Matrices and forms, deals with \(0,\pm 1\) matrices. All the papers have strong connections to the previous sections.

Section 4, Non-euclidean geometry, is the only one with a paper earlier than 1966, namely the joint paper with his thesis supervisor J. Haantjes, announcing the results of the thesis. The other papers all relate geometry to combinatorics.

Obviously, this collection is valuable for researchers working in this area. Since the majority of the reprinted papers appeared in not so readily accessible journals and proceedings, the book should also be a welcome addition to libraries.

Section 1, Graphs and designs, starts with a paper written jointly with the reviewer. This started Seidel’s impressive contributions to the theory of strongly regular graphs and to spherical codes and designs. A proof that Seidel is one of those mathematicians who are at their best when collaborating with others is provided by the fact that 22 of the papers in this book were written with one or more authors. Of these, J.- M. Goethals, Ph. Delsarte, and P. J. Cameron had the strongest influence on his work. In fact 10 of the 14 papers with Goethals occur in these selected works.

Section 2, Lines with few angles, contains work related to two-graphs, including the two important surveys on the subject.

Section 3, Matrices and forms, deals with \(0,\pm 1\) matrices. All the papers have strong connections to the previous sections.

Section 4, Non-euclidean geometry, is the only one with a paper earlier than 1966, namely the joint paper with his thesis supervisor J. Haantjes, announcing the results of the thesis. The other papers all relate geometry to combinatorics.

Obviously, this collection is valuable for researchers working in this area. Since the majority of the reprinted papers appeared in not so readily accessible journals and proceedings, the book should also be a welcome addition to libraries.

Reviewer: J.H.van Lint (Eindhoven)

##### MSC:

05-02 | Research exposition (monographs, survey articles) pertaining to combinatorics |

05E30 | Association schemes, strongly regular graphs |

01A75 | Collected or selected works; reprintings or translations of classics |