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".

External links

*
*
*


Wikimedia Foundation. 2010.

Игры ⚽ Нужна курсовая?

Look at other dictionaries:

  • Dickman function — The Dickman–de Bruijn function ρ(u) plotted on a logarithmic scale. The horizontal axis is the argument u, and the vertical axis is the value of the function. The graph nearly makes a downward line on the logarithmic scale, demonstrating that the …   Wikipedia

  • Dickman-de Bruijn function — In analytic number theory, Dickman s function is a special function used to estimate the proportion of smooth numbers up to a given bound.Dickman s function is named after actuary Karl Dickman, who defined it in his only mathematical publication …   Wikipedia

  • Mathematical constant — A mathematical constant is a special number, usually a real number, that is significantly interesting in some way .[1] Constants arise in many different areas of mathematics, with constants such as e and π occurring in such diverse contexts as… …   Wikipedia

  • List of mathematics articles (G) — NOTOC G G₂ G delta space G networks Gδ set G structure G test G127 G2 manifold G2 structure Gabor atom Gabor filter Gabor transform Gabor Wigner transform Gabow s algorithm Gabriel graph Gabriel s Horn Gain graph Gain group Galerkin method… …   Wikipedia

  • Random permutation statistics — The statistics of random permutations, such as the cycle structure of a random permutation are of fundamental importance in the analysis of algorithms, especially of sorting algorithms, which operate on random permutations. Suppose, for example,… …   Wikipedia

  • Random permutation — A random permutation is a random ordering of a set of objects, that is, a permutation valued random variable. The use of random permutations is often fundamental to fields that use randomized algorithms. Such fields include coding theory,… …   Wikipedia

  • List of permutation topics — This is a list of topics on mathematical permutations.*Alternating group *Alternating permutation *Bijection *Circular shift *Combination *Cycle index *Cycle notation *Cyclic order *Cyclic permutation *Derangement *Even and odd permutations… …   Wikipedia

  • Liste mathematischer Konstanten — Eine mathematische Konstante ist eine fest definierte spezielle reelle oder komplexe Zahl, die sich auf natürliche Weise in der Mathematik ergibt. Anders als physikalische Konstanten werden mathematische Konstanten unabhängig von jedem… …   Deutsch Wikipedia

  • Mathematische Konstanten — Eine mathematische Konstante ist eine fest definierte spezielle reelle oder komplexe Zahl, die sich auf natürliche Weise in der Mathematik ergibt. Anders als physikalische Konstanten werden mathematische Konstanten unabhängig von jedem… …   Deutsch Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”