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Designs 2002 Further Computational and Constructive Design Theory

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ISBN-10: 1402075995

ISBN-13: 9781402075995

Edition: 2nd 2003

Authors: W. D. Wallis

List price: $119.99
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This volume is a sequel to the 1996 compilation, Computational and Constructive Design Theory . It contains research papers and surveys of recent research work on two closely related aspects of the study of combinatorial designs: design construction and computer-aided study of designs. Audience: This volume is suitable for researchers in the theory of combinatorial designs
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Book details

List price: $119.99
Edition: 2nd
Copyright year: 2003
Publisher: Springer
Publication date: 9/30/2003
Binding: Hardcover
Pages: 368
Size: 6.25" wide x 9.25" long x 1.25" tall
Weight: 1.694
Language: English

The Existence of 2-SOLSSOMs
Direct Constructions
Recursive Constructions
Conjugate Orthogonal Diagonal Latin Squares with Missing Subsquares
Direct Construction
Recursive Construction
A General Bound
The Case 2 [less than or equal] n [less than or equal] 6
Combinatorial Trades: a Survey of Recent Results
Introduction and Preliminaries
Trades in designs
Trades in latin squares
Trade uses
Latin representations and trades used in tripartite decompositions
[mu]-way trades
Graphical trades
Future directions
Two-stage Generalized Simulated Annealing for the Construction of Change-Over Designs
Notation and Definitions
A Two Stage Generalized Simulated Annealing Algorithm
Performance of the Two-Stage GSA
New Lower Bounds on the Maximum Number of Mutually Orthogonal Steiner Triple Systems
Starters over Finite Fields
Automorphisms and Hill-climbing
On minimal defining sets in AG(d, 3)
Further Preliminaries
Proof of the Main Theorem
Sets of good hyperplanes in AG(d, 3)
Related critical sets
Hadamard Matrices, Orthogonal designs and Construction Algorithms
Algorithms for constructing Hadamard matrices
On inequivalent Hadamard matrices
Algorithms for constructing orthogonal designs
Short amicable sets and Kharaghani type orthogonal designs
Constructing a Class of Designs with Proportional Balance
Proportionally balanced designs
The method of construction
Feasible parameters for [alpha] = 2, 3 and 4
Constructions motivated by Construction 5
Constructions Using Balanced n-ary Designs
Balanced n-ary Designs
Our Construction
Some Examples
Some Non-existence Results
An Improved Construction
Quadratic Residues
Another Improvement
An Application
More Difference Families
Sets of Steiner Triple Systems of Order 9 Revisited
Large sets
Uniformly intersecting sets
Solving Isomorphism Problems for t-Designs
Moebius Inversions
Extensions of designs
Finding Double Youden Rectangles
Definitions and Literature
Searching for a 13-cyclic 13 X 40 DYR
Further Properties of our new DYRs
Check for Balance
Kirkman Triple Systems and their Generalizations: A Survey
Constructions for Kirkman Triple Systems and Nearly Kirkman Triple Systems for all admissible orders
Early Generalizations
Resolvable Packings and Coverings of v points where v [not identical with] 0 (mod 3)
Other Generalizations
Conclusion and Acknowledgements