Algebraic design theory / Warwick De Launey, Dane Flannery.

Format:

Book

Author/Creator:

De Launey, Warwick, 1958- author.

Flannery, D. L. (Dane Laurence), 1965- author.

Series:

Mathematical surveys and monographs ; Volume 175.

Mathematical surveys and monographs ; Volume 175

Language:

English

Subjects (All):

Combinatorial designs and configurations.

Physical Description:

1 online resource (x, 298 pages).

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2011]

Language Note:

English

Summary:

Combinatorial design theory is a source of simply stated, concrete, yet difficult discrete problems, with the Hadamard conjecture being a prime example. It has become clear that many of these problems are essentially algebraic in nature. This book provides a unified vision of the algebraic themes which have developed so far in design theory. These include the applications in design theory of matrix algebra, the automorphism group and its regular subgroups, the composition of smaller designs to make larger designs, and the connection between designs with regular group actions and solutions to group ring equations. Everything is explained at an elementary level in terms of orthogonality sets and pairwise combinatorial designs--new and simple combinatorial notions which cover many of the commonly studied designs. Particular attention is paid to how the main themes apply in the important new context of cocyclic development. Indeed, this book contains a comprehensive account of cocyclic Hadamard matrices. The book was written to inspire researchers, ranging from the expert to the beginning student, in algebra or design theory, to investigate the fundamental algebraic problems posed by combinatorial design theory.

Contents:

Cover

Title page

Contents

Preface

Announcement

Overview

Many kinds of pairwise combinatorial designs

A primer for algebraic design theory

Orthogonality

Modeling Λ-equivalence

The Grammian

Transposability

New designs from old

Automorphism groups

Group development and regular actions on arrays

Origins of cocyclic development

Group extensions and cocycles

Cocyclic pairwise combinatorial designs

Centrally regular actions

Cocyclic associates

Special classes of cocyclic designs

The Paley matrices

A large family of cocyclic Hadamard matrices

Substitution schemes for cocyclic Hadamard matrices

Calculating cocyclic development rules

Cocyclic Hadamard matrices indexed by elementary abelian groups

Cocyclic concordant systems of orthogonal designs

Asymptotic existence of cocyclic Hadamard matrices

Bibliography

Index

Back Cover.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (pages 287-293) and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

1-4704-1402-3

OCLC:

898199660