《設計理論》是由高等教育出版社出版編著的實體書。《設計理論》是基於一個研究生課程的設計是在對2001南開unversityin彈簧組合中心給出lectare筆記。講稿散落在專家的學生。
基本介紹
- 書名：設計理論
- 原版名稱：Design Theory
- ISBN：9787040241648
- 頁數：221
- 出版社：高等教育出版社
- 出版時間：2009年7月1日
- 裝幀：平裝
- 開本：16
- 叢書名：組合數學叢書
內容簡介,目錄,
內容簡介
The present book is based on the lectare notes of a graduate course DesignTheory which was given at the Center for Combinatorics of Nankai Unversityin spring of 2001. The lecture notes were scattered over the expertsand students.
目錄
Preface
1.BIBDs
1.1 Definition and Fundamental Properties of BIBDs
1.2 Isomorphisms and Automorphisms
1.3 Constructions of New BIBDs from Old Ones
1.4 Exercises
2.Symmetric BIBDs
2.1 Definition and Fundamental Properties
2.2 Bruck-Ryser-Chowla Theorem
2.3 Finite Projective Planes as Symmetric BIBDs
2.4 Difference Sets and Symmetric BIBDs
2.5 Hadamard Matrices and Symmetric BIBDs
2.6 Derived and Residual BIBDs
2.7 Exercises
3.Resolvable BIBDs
3.1 Definitions and Examples
3.2 Finite Affine Planes
3.3 Properties of Resolvable BIBDs
3.4 Exercises
4.Orthogonal Latin Squares
4.1 Orthogonal Latin Squares
4.2 Mutually Orthogonal Latin Squares
4.3 Singular Direct Product of Latin Squares
4.4 Sum Composition of Latin Squares
4.5 Orthogonal Arrays
4.6 Transversal Designs
4.7 Exercises
5.Pairwise Balanced Designs；Group Divisible Designs
5.1 Pairwise Balanced Designs
5.2 Group Divisible Designs
5.3 Closedness of Some Sets of Positive Integers
5.4 Exercises
6.Construction of Some Families of BIBDs
6.1 Steiner Triple Systems
6.2 Cyclic Steiner Triple Systems
6.3 Kirkman Triple Systems
6.4 Triple Systems
6.5 Biplanes
6.6 Exercises
7.t-Designs
7.1 Definition and Fundamental Properties of t-Designs
7.2 Restriction and Extension
7.3 Extendable SBIBDs and Hadamard 3-Designs
7.4 Finite Inversive Planes
7.5 Exercises
8.Steiner Systems
8.1 Steiner Systems
8.2 Some Designs from Hadamard 2-Designs and 3-Designs
8.3 Steiner Systems S(4；11，5) and S(5；12，6)
8.4 Binary Codes
8.5 Binary Golay Codes and Steiner Systems S(4；23，7) and S(5；24,8)
8.6 Exercises
9.Association Schemes and PBIBDs
9.1 Association Schemes
9.2 PBIBDs
9.3 Association Schemes (Continued)
9.4 Exercises
References
