Symmetric Designs An Algebraic Approach / Eric S. Lander.

• CHAPTER 1: SYMMETRIC DESIGNS -- Definitions and simple examples -- 1.2 Hadamard matrices and designs -- 1.3 Projective geometries -- 1.4 t-designs -- 1.5 Dembowski-Wagner Theorem -- CHAPTER 2: AN ALGEBRAIC APPROACH -- 2.1 Existence criteria -- 2.2 The code of a symmetric design -- 2.3 Themodule of a symmetric design -- CHAPTER 3: AUTOMORPHISMS -- 3.1 Fixed points and blocks -- 3.2 Doubly-transitive symmetric designs -- 3.3 Automorphisms of prime order -- 3.4 Counting orbits -- CHAPTER 4: DIFFERENCE SETS -- 4.1 Introduction and examples -- 4.2 Abelian difference sets -- 4.3 Contracting difference sets -- 4.4 G-matrices -- 4.5 Difference sets with multiplier -1 -- 4.6 Cyclic groups are special -- 4.7 More on cyclic groups -- 4.8 Further results -- CHAPTER 5: MULTIPLIER THEOREMS -- 5.1 The automorphism theorem -- 5.2 Contracted automorphism theorem -- 5.3 Blocks fixed by multipliers -- 5.4 Further multiplier theorems -- 5.5 Still further multiplier theorems -- CHAPTER 6: OPEN QUESTIONS -- 6.1 Existence -- 6.2 Cyclic Sylow subgroups -- 6.3 Cyclic projective planes -- 6.4 Multiplier theorems -- 6.5 Tables -- APPENDICES -- A. Permutation Groups -- B. Bilinear and Quadratic Forms -- C. Invariant Factors -- D. Representation Theory -- E. Cyclotomic Fields -- F. P-adic Numbers. 

• Symmetric designs are an important class of combinatorial structures which arose first in the statistics and are now especially important in the study of finite geometries. This book presents some of the algebraic techniques that have been brought to bear on the question of existence, construction and symmetry of symmetric designs - including methods inspired by the algebraic theory of coding and by the representation theory of finite groups - and includes many results. Rich in examples and containing over 100 problems, the text also provides an introduction to many of the modern algebraic approaches used, through six lengthy appendices and supplementary problems. The book will be of interest to both combinatorialists and algebraists, and could be used as a course text for a graduate course

Ämnesord

Combinatorial designs and configurations.  (LCSH)

Publikations- och innehållstyp

511/.6 (DDC)

Tce (kssb/8 (machine generated))