Combinatorics | Permutations

Langford pairing

In combinatorial mathematics, a Langford pairing, also called a Langford sequence, is a permutation of the sequence of 2n numbers 1, 1, 2, 2, ..., n, n in which the two 1s are one unit apart, the two 2s 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. (Wikipedia).

Langford pairing
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Related pages

Permutation | Multiplication | Stirling permutation | The Art of Computer Programming | Mathematics | Combinatorics | Discrete Mathematics (journal) | Modular arithmetic