Design theory. Vol. I. 2nd ed. (English) Zbl 0945.05004

Beth, Thomas; Jungnickel, Dieter; Lenz, Hanfried

Encyclopedia of Mathematics and Its Applications. 69. Cambridge: Cambridge University Press. xix, 607 p. (1999).

This two-volume set is a thoroughly revised and expanded version of the first edition of the same authors’ book [Design theory (Bibliographisches Institut, B.I.-Wissenschaftsverlag, Mannheim, Wien, Zürich) (1985; Zbl 0569.05002)]. In the fourteen years since the appearance of the first edition, design theory has undergone an extensive and explosive development, both in depth and breadth. This is duly reflected in this second edition whose several parts have been completely rewritten, and often expanded. In particular, Chapter VI dealing with difference sets has increased in size almost fourfold. One completely new, and quite substantial, chapter has been added (Chapter XIII, Applications of designs).
The value of these two volumes as a reference work for any researcher or student of design theory, or indeed, any combinatorial mathematician, cannot be overstated, in spite of the authors’ disclaimer (in the Foreword) that it is not intended to meet encyclopedic standards. The effort that was put (primarily by the second author) into rewriting the individual chapters will no doubt benefit the reader who will find this new edition not only updated and expanded but also much better readable.

Reviewer: A.Rosa (Hamilton/Ontario)

MSC:

05-02	Research exposition (monographs, survey articles) pertaining to combinatorics
05B05	Combinatorial aspects of block designs
62K10	Statistical block designs
05B10	Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
05B15	Orthogonal arrays, Latin squares, Room squares
05B30	Other designs, configurations

Keywords:

difference sets; design theory