Alternating permutation

Type of permutation

In combinatorial mathematics, an alternating permutation of the set {1, 2, 3, ..., n} is a permutation (arrangement) of those numbers so that each entry is alternately greater or less than the preceding entry. For example, the five alternating permutations of {1, 2, 3, 4} are:1, 3, 2, 4 because 1 < 3 > 2 < 4, 1, 4, 2, 3 because 1 < 4 > 2 < 3, 2, 3, 1, 4 because 2 < 3 > 1 < 4, 2, 4, 1, 3 because 2 < 4 > 1 < 3, and 3, 4, 1, 2 because 3 < 4 > 1 < 2.

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