## Latin squares and their applications |

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### Contents

Preface | 11 |

Special types of latin square | 57 |

Generalizations of latin squares | 95 |

Copyright | |

15 other sections not shown

### Common terms and phrases

abelian group Amer autotopism Cayley table cells code words Combinatorial complete latin square complete mapping complete set construction contains Corollary corresponding cyclic group defined denote diagonal latin squares disjoint element of G entries equation example exist follows given gonal graph group G group of order groupoid idempotent identity element implies integer isomorphic isotopic latin rectangles latin subsquare lines loop magic squares Math matrix modulo multiplication table mutually orthogonal latin obtained odd order ordered pair orthogonal array orthogonal latin squares pair of orthogonal parallel classes permutation plane of order points positive integer prime problem Proof proved quadrangle criterion quasigroup quasigroup of order R. C. Bose represented result Room squares rows and columns S. S. Shrikhande Sade set of mutually square Lx squares of order Steiner triple systems subset symbols symmetric latin square theorem total number transversal unique vertex vertices