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Langford pairing : ウィキペディア英語版 | Langford pairing
In combinatorial mathematics, a Langford pairing, also called a Langford sequence, is a permutation of the sequence of 2''n'' numbers 1, 1, 2, 2, ..., ''n'', ''n'' in which the two ones are one unit apart, the two twos are two units apart, and more generally the two copies of each number ''k'' are ''k'' units apart. Langford pairings are named after C. Dudley Langford, who posed the problem of constructing them in 1958. Langford's problem is the task of finding Langford pairings for a given value of ''n''.〔; .〕 The closely related concept of a Skolem sequence is defined in the same way, but instead permutes the sequence 0, 0, 1, 1, ..., ''n'' − 1, ''n'' − 1. == Example ==
For example, a Langford pairing for ''n'' = 3 is given by the sequence 2,3,1,2,1,3.
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