The CRC handbook of combinatorial designs. 2nd ed. (English) Zbl 1101.05001

Colbourn, Charles J. (ed.); Dinitz, Jeffrey H. (ed.)

Discrete Mathematics and its Applications. Boca Raton, FL: Chapman & Hall/CRC (ISBN 1-58488-506-8/hbk). 984 p. (2007).

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The new articles added to this second edition will be reviewed individually.
The articles of the first edition (1996) were reviewed individually (see Zbl 0836.00010).
The publisher: Continuing in the bestselling, informative tradition of the first edition, the Handbook of Combinatorial Designs, Second Edition remains the only resource to contain all of the most important results and tables in the field of combinatorial design. This handbook covers the constructions, properties, and applications of designs as well as existence results.

Over 30% longer than the first edition, the book builds upon the groundwork of its predecessor while retaining the original contributors’ expertise. The first part contains a brief introduction and history of the subject. The following parts focus on four main classes of combinatorial designs: balanced incomplete block designs, orthogonal arrays and Latin squares, pairwise balanced designs, and Hadamard and orthogonal designs. Closely connected to the preceding sections, the next part surveys 65 additional classes of designs, such as balanced ternary, factorial, graphical, Howell, quasi-symmetric, and spherical. The final part presents mathematical and computational background related to design theory.

New to the Second Edition:
– An introductory part that provides a general overview and a historical perspective of the area
– New chapters on the history of design theory, various codes, bent functions, and numerous types of designs
– Fully updated tables, including BIBDs, MOLS, PBDs, and Hadamard matrices
– Nearly 2,200 references in a single bibliographic section

Meeting the need for up-to-date and accessible tabular and reference information, this handbook provides the tools to understand combinatorial design theory and applications that span the entire discipline.

MSC:

05-02	Research exposition (monographs, survey articles) pertaining to combinatorics
00B15	Collections of articles of miscellaneous specific interest
05Bxx	Designs and configurations