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Orthogonal Latin Squares Based on Groups von Anthony B. Evans

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ISBN: 978-3-319-94429-6
Einband: Fester Einband
Verfügbarkeit: Lieferbar in ca. 20-45 Arbeitstagen
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This monograph presents a unified exposition of latin squares and mutually orthogonal sets of latin squares based on groups. Its focus is on orthomorphisms and complete mappings of finite groups, while also offering a complete proof of the Hall-Paige conjecture. The use of latin squares in constructions of nets, affine planes, projective planes, and transversal designs also motivates this inquiry.  

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. 

This monograph presents a unified exposition of latin squares and mutually orthogonal sets of latin squares based on groups. Its focus is on orthomorphisms and complete mappings of finite groups, while also offering a complete proof of the Hall-Paige conjecture. The use of latin squares in constructions of nets, affine planes, projective planes, and transversal designs also motivates this inquiry.  

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. 

AutorEvans, Anthony B.
EinbandFester Einband
Erscheinungsjahr2018
Seitenangabe537 S.
LieferstatusLieferbar in ca. 20-45 Arbeitstagen
AusgabekennzeichenEnglisch
AbbildungenXV, 537 p. 90 illus., schwarz-weiss Illustrationen
MasseH23.5 cm x B15.5 cm x D3.5 cm 992 g
CoverlagSpringer (Imprint/Brand)
Auflage1st ed. 2018
ReiheDevelopments in Mathematics
VerlagSpringer Nature EN

Alle Bände der Reihe "Developments in Mathematics"

Über den Autor Anthony B. Evans

?Anthony B. Evans is Professor of Mathematics at Wright State University in Dayton, Ohio. Since the mid 1980s, his primary research has been on orthomorphisms and complete mappings of finite groups and their applications. These mappings arise in the study of mutually orthogonal latin squares that are derived from the multiplication tables of finite groups. As an offshoot of this research, he has also worked on graph representations. His previous book, Orthomorphism Graphs of Groups (1992), appeared in the series, Lecture Notes in Mathematics.

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