Finite Geometry and Character Theory

✍ Scribed by Alexander Pott (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1995
• Tongue: English
• Leaves: 188
• Series: Lecture Notes in Mathematics 1601
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Preliminaries: Incidence structures with singer groups....Pages 1-33
Examples: Existence and non-existence....Pages 35-68
Difference sets with classical parameters....Pages 69-102
Semiregular relative difference sets....Pages 103-111
Projective planes with quasiregular collineation groups....Pages 113-147
Codes and sequences....Pages 149-168

✦ Subjects

Combinatorics; Geometry; Group Theory and Generalizations; Coding and Information Theory