SQUARE X-LINKED DESIGNSt
نویسنده
چکیده
A A-linked design is an abstract system of v 'points' and b lines' such that every two points are joined by exactly A lines. A partial classification is given of those extremal examples with b = v, and necessary and sufficient conditions are proved for them to be of each of the only two non-trivial types known, namely square BIBDs and point-complemented square BIBDs. For each A > 1 the number of examples not of the first type is finite. A partial classification is also given of A-linked designs with one more line than points, in which every point has the same number of lines. Finally, if the points and lines of a A-linked design are divided into v' and b' classes respectively, and the number of points of any class on a line depends only on the class of the line, then b' ^ v', and if b' = v' the division is a tactical decomposition.
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