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2018 | OriginalPaper | Chapter

1. Latin Squares Based on Groups

Author : Anthony B. Evans

Published in: Orthogonal Latin Squares Based on Groups

Publisher: Springer International Publishing

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Abstract

Latin squares and orthogonal Latin squares have been used in the construction of many classes of designs: nets, affine planes, projective planes, and transversal designs, in particular. When orthogonal sets of Latin squares are obtained from the multiplication table of a finite group by permuting columns, each square is determined by its first row, which is a permutation of the elements of the group. This enables us to describe and study orthogonality from a purely algebraic point of view, using difference matrices, complete mappings, and orthomorphisms. The nets, affine planes, projective planes, and transversal designs constructed in this way are characterized by the action of the group on these designs. We introduce these concepts in this chapter.

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next chapter When Is a Latin Square Based on a Group?
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Metadata
Title
Latin Squares Based on Groups
Author
Anthony B. Evans
Copyright Year
2018
Book
Orthogonal Latin Squares Based on Groups

Print ISBN: 978-3-319-94429-6

Electronic ISBN: 978-3-319-94430-2

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-94430-2_1

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