Authors:
- Presents the first unified proof of the Hall–Paige conjecture
- Discusses the actions of groups on designs derived from latin squares
- Includes an extensive list of open problems on the construction and structure of orthomorphism graphs suitable for researchers and graduate students
Part of the book series: Developments in Mathematics (DEVM, volume 57)
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Table of contents (16 chapters)
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Front Matter
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Introduction
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Front Matter
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Orthomorphism Graphs of Groups
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Front Matter
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Additional Topics
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Front Matter
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About this book
The text begins by introducing fundamental concepts, like the tests for determining whether a latin square is based on a group, as well as orthomorphisms and complete mappings. From there, it describes the existence problem for complete mappings of groups, building up to the proof of the Hall–Paige conjecture. The third part presents a comprehensive study of orthomorphism graphs of groups, while the last part provides a discussion of Cartesian projective planes, related combinatorial structures, and a list of open problems.
Expanding the author’s 1992 monograph, Orthomorphism Graphs of Groups, this book is an essential reference tool for mathematics researchers or graduate students tackling latin square problems in combinatorics. Its presentation draws on a basic understanding of finite group theory, finite field theory, linear algebra, and elementary number theory—more advanced theories are introduced in the text as needed.
Authors and Affiliations
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Mathematics and Statistics, Wright State University, Dayton, USA
Anthony B. Evans
About the author
Bibliographic Information
Book Title: Orthogonal Latin Squares Based on Groups
Authors: Anthony B. Evans
Series Title: Developments in Mathematics
DOI: https://doi.org/10.1007/978-3-319-94430-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Hardcover ISBN: 978-3-319-94429-6Published: 05 September 2018
Softcover ISBN: 978-3-030-06850-9Published: 20 December 2018
eBook ISBN: 978-3-319-94430-2Published: 17 August 2018
Series ISSN: 1389-2177
Series E-ISSN: 2197-795X
Edition Number: 1
Number of Pages: XV, 537
Number of Illustrations: 90 b/w illustrations