Orthogonal Latin squares based on groups /

Orthogonal Latin squares based on groups /

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Bibliographic Details
Author / Creator:	Evans, Anthony B., 1949- author.
Imprint:	Cham, Switzerland : Springer, 2018.
Description:	1 online resource (xv, 537 pages) : illustrations
Language:	English
Series:	Developments in mathematics, 1389-2177 ; volume 57 Developments in mathematics ; v. 57.
Subject:	Magic squares. Magic squares. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11690348

Hidden Bibliographic Details
ISBN:	9783319944302 3319944304 9783319944296 3319944290 9783319944319 3319944312 9783030068509 3030068501
Digital file characteristics:	text file PDF
Notes:	Includes bibliographical references and index. Online resource; title from PDF title page (SpringerLink, viewed August 21, 2018).
Summary:	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.--
Other form:	Print version: Evans, Anthony B., 1949- Orthogonal Latin squares based on groups. Cham, Switzerland : Springer, 2018 3319944290 9783319944296
Standard no.:	10.1007/978-3-319-94430-2 10.1007/978-3-319-94

Description
Summary:	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. <br> 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. <br> 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. <br>
Physical Description:	1 online resource (xv, 537 pages) : illustrations
Bibliography:	Includes bibliographical references and index.
ISBN:	9783319944302 3319944304 9783319944296 3319944290 9783319944319 3319944312 9783030068509 3030068501
ISSN:	1389-2177 ;