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Algorithms in Combinatorial Design Theory (Mathematics Studies)

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Recent years have seen an explosive growth in research in combinatorics and graph theory. One primary factor in this rapid development has been the advent of computers, and the parallel study of practical and efficient algorithms. This volume represents an attempt to sample current research in one branch of combinatorics, namely combmatorial design theory, which is algorithmic in nature.

Combmatorial design theory is that branch of combinatorics which is concerned with the construction and analysis of regular f h t e configurations such as projective planes, Hadamard matrices, block designs, and the like. Historically, design theory has borrowed tools from algebra, geometry and number theory to develop direct constructions of designs. These are typically supplemented by recursive ~ ~ n s t ~ ~ t iwohnichs ,a re in fact algorithms for constructing larger designs from =me smaller ones. This lent an algorithmic flavour to the construction of designs, even before the advent of powerful computers.

Computers have had a definite and long-lasting impact on research in combinatorial design theory. Rimarily, the speed of present day computers has enabled researchers to construct many designs whose discovery by hand would have been difficuit if not imposslile. A second important consequence has been the vastly improved capability for anu&sis of designs. This includes the detection of isomorphism, and hence gives us a vehicle for addressing enumeration questions. It a h includes the determination of various properties of designs; examples include resolvability, colouring, decomposition, and subdesigns. Although in principle all such properties are computable by hand, research on designs with additional properties has burgeoned largely because of the availability of computational assistance.
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