Design theory / C. C. Lindner, C. A. Rodger.
Series The CRC Press series on discrete mathematics and its applicationsEditor: Boca Raton : CRC Press, c1997Descripción: 198 p. : il. ; 25 cmISBN: 0849339863Otra clasificación: 05-01 (05B05)1 Steiner Triple Systems [1] 1.1 The existence problem [1] 1.2 v = 3 (mod 6): The Bose Construction [4] 1.3 v = 1 (mod 6): The Skolem Construction [9] 1.4 v = 5 (mod 6): The 6n + 5 Construction [14] 1.5 Quasigroups with holes and Steiner triple systems [17] 1.5.1 Constructing quasigroups with holes [17] 1.5.2 Constructing Steiner triple systems using quasigroups with holes [22] 1.6 The Wilson Construction [27] 1.7 Cyclic Steiner triple systems [31] 2 A-Fold Triple Systems [37] 2.1 Triple systems of index A > 1 [37] 2.2 The existence of idempotent latin squares [39] 2.3 2-Fold triple systems [42] 2.3.1 Constructing 2-fold triple systems [42] 2.4 A = 3 and 6 [47] 2.5 A-Fold triple systems in general [50] 3 Maximum Packings and Minimum Coverings [53] 3.1 The general problem [53] 3.2 Maximum packings [58] 3.3 Minimum coverings [63] 4 Kirkman Triple Systems [71] 4.1 A recursive construction [71] 4.2 Constructing pairwise balanced designs [79] 5 Mutually Orthogonal Latin Squares [93] 5.1 Introduction [93] 5.2 The Euler and MacNeish Conjectures [97] 5.3 Disproof of the MacNeish Conjecture [110] 5.4 Disproof of the Euler Conjecture [113] 5.5 Orthogonal latin squares of order n = 2 (mod 4) [116] 6 Affine and Projective Planes [131] 6.1 Affine planes [131] 6.2 Projective planes [133] 6.3 Connections between affine and projective planes [135] 6.4 Connection between affine planes and complete sets of MOLS(n) [137] 6.5 Coordinatizing the affine plane [140] 7 Steiner Quadruple Systems [145] 7.1 Introduction [145] 7.2 Constructions of Steiner Quadruple Systems [153] 7.3 The Stern and Lenz Lemma [158] 7.4 The (3v — 2u)~Construction [167] Appendices [185] A Cyclic Steiner Triple Systems [187] B Answers to Selected Exercises [189]
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 05 L747 (Browse shelf) | Available | A-7734 |
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| 05 K21e Ejercicios de combinatoria con soluciones / | 05 K21e Ejercicios de combinatoria con soluciones / | 05 K82 Theorie der endlichen und unendlichen Graphen : | 05 L747 Design theory / | 05 L896 Matching theory / | 05 M167 Combinatory analysis / | 05 M367 Applied graph theory / |
Includes bibliographical references (p. 195-196) and index.
1 Steiner Triple Systems [1] --
1.1 The existence problem [1] --
1.2 v = 3 (mod 6): The Bose Construction [4] --
1.3 v = 1 (mod 6): The Skolem Construction [9] --
1.4 v = 5 (mod 6): The 6n + 5 Construction [14] --
1.5 Quasigroups with holes and Steiner triple systems [17] --
1.5.1 Constructing quasigroups with holes [17] --
1.5.2 Constructing Steiner triple systems using quasigroups with holes [22] --
1.6 The Wilson Construction [27] --
1.7 Cyclic Steiner triple systems [31] --
2 A-Fold Triple Systems [37] --
2.1 Triple systems of index A > 1 [37] --
2.2 The existence of idempotent latin squares [39] --
2.3 2-Fold triple systems [42] --
2.3.1 Constructing 2-fold triple systems [42] --
2.4 A = 3 and 6 [47] --
2.5 A-Fold triple systems in general [50] --
3 Maximum Packings and Minimum Coverings [53] --
3.1 The general problem [53] --
3.2 Maximum packings [58] --
3.3 Minimum coverings [63] --
4 Kirkman Triple Systems [71] --
4.1 A recursive construction [71] --
4.2 Constructing pairwise balanced designs [79] --
5 Mutually Orthogonal Latin Squares [93] --
5.1 Introduction [93] --
5.2 The Euler and MacNeish Conjectures [97] --
5.3 Disproof of the MacNeish Conjecture [110] --
5.4 Disproof of the Euler Conjecture [113] --
5.5 Orthogonal latin squares of order n = 2 (mod 4) [116] --
6 Affine and Projective Planes [131] --
6.1 Affine planes [131] --
6.2 Projective planes [133] --
6.3 Connections between affine and projective planes [135] --
6.4 Connection between affine planes and complete sets of MOLS(n) [137] --
6.5 Coordinatizing the affine plane [140] --
7 Steiner Quadruple Systems [145] --
7.1 Introduction [145] --
7.2 Constructions of Steiner Quadruple Systems [153] --
7.3 The Stern and Lenz Lemma [158] --
7.4 The (3v — 2u)~Construction [167] --
Appendices [185] --
A Cyclic Steiner Triple Systems [187] --
B Answers to Selected Exercises [189] --
MR, REVIEW #
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