1st Edition

Frames and Resolvable Designs
Uses, Constructions and Existence

ISBN 9780849339844
Published June 10, 1996 by CRC Press
256 Pages

USD $195.00

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Book Description

Frames, together with a modified fundamental construction, provide a powerful recursive mechanism for constructing resolvable balanced incomplete block designs (BIBDs). Frames and Resolvable Designs: Uses, Constructions and Existence presents a unique study of frames and their application to this construction.

Chapter 1 sets the stage by describing the games combinatorialists play. It introduces basic combinatorial structures and construction techniques. Chapter 2 discusses frames extensively and includes comprehensive lists of direct and recursive constructions. Chapter 3 provides known classes of RBIBD constructions. Chapter 4 deals with existence results and demonstrates the utility of the frame approach. Chapter 5 is a series of informative tables useful for researchers.

No other book tackles this demanding topic from these varied perspectives. Multi-faceted and written for easy access by different users, Frames and Resolvable Designs: Uses, Constructions and Existence is the right choice for students, as a text in advanced design theory; for researchers, as a resource complement to standard encyclopedic works; and for mathematicians and statisticians in this field, as a working handbook.

Table of Contents

The Rules
The Games
Latin Squares
Group Divisible Designs
Experimental Designs
Frame Constructions
Necessary Conditions
Frames and Other Types of Designs
Recursive Constructions
Near Resolvable Designs
Some Direct Constructions
Constructions for Resolvable Designs
Constructions Using Finite Geometries
Constructions Using Differences
Constructions Using Frames
Constructions Using RGDDs
Constructions Using Color Classes
Constructions Using SOLSSOMs
A Few More Constructions
Existence Results
Known Results
An Approach For Asymptotic Results
New Results, k = 5
New Results, k = 6
New Results, k = 7
New Results, k = 8
Near Resolvable Designs
Resolvable BIBDs, 10 = v = 100
Resolvable BIBDs, 101 = v = 200
Table of Symbols

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Furino\, Steven; Ying\, Miao; Jianxing\, Yin