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Introduction to combinatorial designs

Author: W D Wallis
Publisher: Boca Raton : Chapman & Hall/CRC, ©2007.
Series: Discrete mathematics and its applications.
Edition/Format:   Print book : English : 2nd edView all editions and formats
Summary:
"Reflecting recent results in design theory and outlining several applications, this new edition of a standard text presents a comprehensive look at the combinatorial theory of experimental design. Suitable for a one-semester course or for self-study, it will prepare readers for further exploration in the field."--Jacket.
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Additional Physical Format: Online version:
Wallis, W.D.
Introduction to combinatorial designs.
Boca Raton : Chapman & Hall/CRC, ©2007
(OCoLC)681674980
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: W D Wallis
ISBN: 9781584888383 1584888385
OCLC Number: 80917785
Notes: Revised edition of: Combinatorial designs. c1988.
Description: xvi, 311 pages : illustrations ; 25 cm.
Contents: Basic concepts. Combinatorial designs ; Some examples of designs ; Block designs ; Systems of distinct representatives --
Balanced designs. Pairwise balanced designs ; Balanced incomplete block designs ; Another proof of Fisher's inequality ; t-Designs --
Finite geometries. Finite affine planes ; Finite fields ; Construction of finite affine geometries ; Finite projective geometries --
Some properties of finite geometries. Ovals in projective planes ; The Desargues configuration --
Difference sets and difference methods. Difference sets ; Construction of difference sets ; Properties of difference sets ; General difference methods ; Singer difference sets --
More about block designs. Residual and derived designs ; Resolvability --
The main existence theorem. Sums of squares ; The Bruck-Ryser-Chowla theorem ; Another proof --
Latin squares. Latin squares and subsquares ; Orthogonality ; Idempotent Latin squares ; Transversal designs --
More about orthogonality. Spouse-avoiding mixed doubles tournaments ; Three orthogonal Latin squares ; Bachelor squares --
One-factorizations. Basic ideas ; The variability of one-factorizations ; Starters --
Applications of one-factorizations. An application to finite projective planes ; Tournament applications of one-factorizations ; Tournaments balanced for carryover --
Steiner triple systems. Construction of triple systems ; Subsystems ; Simple triple systems ; Cyclic triple systems ; Large sets and related designs --
Kirkman triple systems and generalizations. Kirkman triple systems ; Kirkman packings and coverings --
Hadamard matrices. Basic ideas ; Hadamard matrices and block designs ; Further Hadamard matrix constructions ; Regular Hadamard matrices ; Equivalence --
Room squares. Definitions ; Starter constructions ; Subsquare constructions ; The existence theorem ; Howell rotations --
Further applications of design theory. Statistical applications ; Information and cryptography ; Golf designs.
Series Title: Discrete mathematics and its applications.
Responsibility: W.D. Wallis.
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Abstract:

Offers an introduction to the areas of design theory as well as to more contemporary designs based on applications in a variety of fields. This work also introduces balanced designs and finite  Read more...

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