Frames and Resolvable Designs: Uses, Constructions and Existence, 1st Edition (Hardback) book cover

Frames and Resolvable Designs

Uses, Constructions and Existence, 1st Edition

By Steven Furino, Miao Ying, Yin Jianxing

CRC Press

256 pages

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Hardback: 9780849339844
pub: 1996-06-10
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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


About the Authors/Editor

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

About the Series

Discrete Mathematics and Its Applications

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
COMPUTERS / Operating Systems / General
MATHEMATICS / Combinatorics