Designs 2002: Further Computational and Constructive Design TheoryW.D. Wallis This volume is a sequel to our 1996 compilation, Computational and Constructive Design Theory. Again we concentrate on two closely re lated aspects of the study of combinatorial designs: design construction and computer-aided study of designs. There are at least three classes of constructive problems in design theory. The first type of problem is the construction of a specific design. This might arise because that one particular case is an exception to a general rule, the last remaining case of a problem, or the smallest unknown case. A good example is the proof that there is no projective plane of parameter 10. In that case the computations involved were not different in kind from those which have been done by human brains without electronic assistance; they were merely longer. Computers have also been useful in the study of combinatorial spec trum problems: if a class of design has certain parameters, what is the set of values that the parameters can realize? In many cases, there is a recursive construction, so that the existence of a small number of "starter" designs leads to the construction of infinite classes of designs, and computers have proven very useful in finding "starter" designs. |
Contents
| 7 | |
Conjugate Orthogonal Diagonal Latin Squares with Missing Subsquares | 23 |
4 | 54 |
Twostage Generalized Simulated Annealing for the Construction | 69 |
5 | 75 |
71 | 98 |
Diane Donovan Abdollah Khodkar and Anne Penfold Street | 104 |
Hadamard Matrices Orthogonal designs and Construction Algorithms | 132 |
11 | 270 |
Solving Isomorphism Problems for tDesigns | 277 |
K Phillips and D A Preece 1 Introduction | 301 |
Definitions and Literature | 302 |
Searching for a 13cyclic 13 x 40 DYR | 306 |
Isomorphism | 309 |
Further Properties of our new DYRS | 313 |
Check for Balance | 314 |
F 2 2 | 162 |
73 | 177 |
8 | 194 |
75 | 198 |
83 | 205 |
Constructing a Class of Designs with Proportional Balance | 207 |
Constructions Using Balanced nary Designs | 226 |
92 | 233 |
Sets of Steiner Triple Systems of Order 9 Revisited | 255 |
13 | 315 |
A Survey | 317 |
Rolf S Rees W D Wallis 1 Introduction | 318 |
Constructions for Kirkman Triple Systems and Nearly Kirk man Triple Systems for all admissible orders | 334 |
Early Generalizations | 342 |
Resolvable Packings and Coverings of v points where v 0 | 348 |
Other Generalizations | 359 |
Conclusion and Acknowledgements | 363 |
Other editions - View all
Designs 2002: Further Computational and Constructive Design Theory W.D. Wallis No preview available - 2012 |
Common terms and phrases
2-HSOLSSOM AG(d algorithm array automorphism group b₁ balanced ternary base blocks BiBD block design block of H block size circulant matrices Combin Combinatorial Designs complete condition contains corresponding cosets critical set denote diagonal disjoint elements Example exists GDD of type GF(q give given graph Hadamard matrices Hamming distance distribution holes hyperplane of H incidence matrix inequivalent Hadamard matrices integer intersection isomorphism Kharaghani Kirkman Triple Systems Koukouvinos large sets latin trade Lemma matrices of order minimal defining set multipliers NPAF obtain occurs orthogonal design orthogonal STS pairs parallel class parameters partial latin square partial Steiner latin permutation prime power projections Proof proportionally balanced design satisfy Seberry set of order simulated annealing square of order Steiner latin square Steiner triple systems subsets Suppose symmetric Hamming distance T₁ Theorem trade of volume trade volumes variables wsub zero