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Books > Science & Mathematics > Mathematics > Combinatorics & graph theory
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Orthogonal Latin Squares Based on Groups (Hardcover, 1st ed. 2018)
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Orthogonal Latin Squares Based on Groups (Hardcover, 1st ed. 2018)
Series: Developments in Mathematics, 57
Expected to ship within 10 - 15 working days
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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.
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