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Finite Geometry and Character Theory : Research Reports Esprit - Alexander Pott

Finite Geometry and Character Theory

Research Reports Esprit

Paperback Published: 6th April 1995
ISBN: 9783540590651
Number Of Pages: 188

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Difference sets are of central interest in finite geometry and design theory. One of the main techniques to investigate abelian difference sets is a discrete version of the classical Fourier transform (i.e., character theory) in connection with algebraic number theory. This approach is described using only basic knowledge of algebra and algebraic number theory. It contains not only most of our present knowledge about abelian difference sets, but also gives applications of character theory to projective planes with quasiregular collineation groups. Therefore, the book is of interest both to geometers and mathematicians working on difference sets. Moreover, the Fourier transform is important in more applied branches of discrete mathematics such as coding theory and shift register sequences.

Preliminariesp. 1
Basic definitionsp. 1
Algebraic toolsp. 16
Multipliersp. 27
Examplesp. 35
Difference setsp. 35
Relative difference setsp. 40
Divisible difference setsp. 49
Non-existence resultsp. 56
Classical Parametersp. 69
Singer difference setsp. 69
The Gordon-Mills-Welch constructionp. 75
The Waterloo problemp. 95
Semiregular relative difference setsp. 103
Necessary conditionsp. 104
Examples and characterizationsp. 108
Quasiregular collineation groupsp. 113
Introductionp. 113
Affine difference setsp. 115
Direct product difference setsp. 130
Planar functionsp. 141
Codes and sequencesp. 149
Perfect sequencesp. 149
Almost perfect sequencesp. 153
Abelian difference set codesp. 157
Bibliographyp. 169
Indexp. 180
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540590651
ISBN-10: 354059065X
Series: Research Reports Esprit
Audience: General
Format: Paperback
Language: English
Number Of Pages: 188
Published: 6th April 1995
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.07
Weight (kg): 0.28