A pair design is an ordering of the [image omitted] pairs from n elements so that no two occurrences of any element have fewer than the obvious maximum-minimum of [image omitted] pairs separating them. If Sn is the set of adjacent pairs in the cycle Cn starting with (1, 2) and P is the permutation (l)(3, 5, 7, …, 6, 4, 2) it is proven that [image omitted] is a pair design, where [image omitted] for n odd and L = n-2 for n even It is also shown that for n odd all pair designs are equivalent under permutation of element labels and reverse ordering of the pairs in the design. On the other hand, for n even, there are already, 7,360 inequivalent classes of pair designs for n = 6, and the number of classes for n = 8 has thus far defied enumeration using a CDC 7600 computer.
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