Golomb–Dickman constant

Golomb–Dickman constant

In mathematics, the Golomb–Dickman constant arises in the theory of random permutations. Let "a""n" be the average — taken over all permutations of a set of size "n" — of the length of the longest cycle in each permutation. Then the Golomb–Dickman constant is

: lim_{n oinfty} frac{a_n}{n} =0.62432 99885 43550 87099 29363 83100 83724dots.

In the language of probability theory, "a""n" is the expected length of the longest cycle in a uniformly distributed random permutation of a set of size "n".

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