Alternating permutation
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In combinatorial mathematics, an alternating permutation of the set {1, 2, 3, ..., n} is an arrangement of those numbers into an order c1, ..., cn such that no element ci is between ci − 1 and ci + 1 for any value of i and c1< c2.
Let An be the number of alternating permutations of the set {1, ..., n}. Then the exponential generating function of this sequence of numbers is a trigonometric function:
Consequently the numbers A2n with even indices are called secant numbers and those with odd indices are called tangent numbers.
[edit] See also
[edit] References
- André, D. "Développements de sec x et tan x." Comptes Rendus Acad. Sci., Paris 88, 965-967, 1879.
- André, D. "Mémoire sur les permutations alternées." J. Math. 7, 167-184, 1881.
