Allowable sequences are sequences of pemutations of a set of elements. The change from one permutation in the sequence to the next consists of reversing one or more disjoint portions of the permutation. Some allowable sequences can be "realized" by arranging their elements as points on a plane. The permutations then correspond to projections of the points onto a plane in a certain direction in which the projections of the points are all distinct, and the sequence corresponds to all these projections as the direction is rotated through 180 degrees.
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