Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices
W. D. Wallis, A. P. Street, J. S. Wallis, "Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices"
1972 | pages: 494 | ISBN: 3540060359 | DJVU | 3,3 mb
1972 | pages: 494 | ISBN: 3540060359 | DJVU | 3,3 mb
This is probably as close as we can come to a working definition. One then sees three basic areas:
(i) the theory of enumeration, wherein the "specified rules" are quite simple and it is required to find the number of essentially different ways in which the arrangement can be carried out;
(ii) discrete optimization such as linear programming; again the rules are simple but the problem is to find the "best" way of carrying them out according to some criterion;
(iii) the theory of designs, patterns and configurations, in which the rules are more demanding, where the basic problems are whether or not the objects can be arranged in a certain configuration and whether or not the configurations contain certain special features.
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