Author(s): Anthony B. Evans
Series: Lecture Notes in Mathematics
Edition: 1
Publisher: Springer
Year: 1993
Language: English
Pages: 122
Contents......Page 5
Preface......Page 4
1. Definitions and elementary results......Page 7
2. Latin squares and difference matrices......Page 11
3. Nets and affine planes......Page 15
4. Neofields......Page 20
5. The existence problem......Page 24
1. Introduction......Page 31
2. A linear algebra approach......Page 32
3. A special class of examples......Page 34
4. Systems of order 5 or less......Page 36
1. Linear and quadratic orthomorphisms......Page 41
2. Cyclotomic orthomorphisms......Page 46
3. Permutation polynomials......Page 49
4. Cyclotomy and permutation polynomials......Page 53
1. Introduction......Page 56
2. Orthomorphisms from automorphisms......Page 57
3. Bounds on \omega(A(G) \cup A^-(G))......Page 58
4. The abelian case......Page 60
1. Powers......Page 63
2. Strong complete mappings......Page 66
3. Difference sets......Page 69
4. Maximal sets of orthomorphisms......Page 73
5. Complete sets of orthomorphisms......Page 79
1. Introduction......Page 83
2. Groups of order 8......Page 84
3. Groups of order 9......Page 87
4. The cyclic group of order 11......Page 88
5. Groups of order at least 12......Page 91
2. Orthomorphism graphs......Page 97
3. Structure of orthomorphism graphs......Page 103
4. Cliques of orthomorphism graphs......Page 106
References......Page 111
Index......Page 116
