DERANGEMENTS - definizione. Che cos'è DERANGEMENTS
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Cosa (chi) è DERANGEMENTS - definizione

PERMUTATION OF A SET WHICH LEAVES NO MEMBER IN ITS ORIGINAL PLACE
Subfactorial; Hat-check problem; Derangements; Sub-factorial
  • <math>\int_0^\infty(t-1)^ze^{-t}dt</math> in the complex plane
  • The 9 derangements (from 24 permutations) are highlighted.

derangement         
Derangement is the state of being mentally ill and unable to think or act in a controlled way. (OLD-FASHIONED)
N-UNCOUNT
Derangement         
·noun The act of deranging or putting out of order, or the state of being deranged; disarrangement; disorder; confusion; especially, mental disorder; insanity.
derangement         
n.
1.
Disorder, confusion, disarrangement.
2.
Disturbance, discomposure.
3.
Insanity, lunacy, madness, mania, dehrium, mental aberration, mental alienation, alienation.

Wikipedia

Derangement

In combinatorial mathematics, a derangement is a permutation of the elements of a set in which no element appears in its original position. In other words, a derangement is a permutation that has no fixed points.

The number of derangements of a set of size n is known as the subfactorial of n or the n-th derangement number or n-th de Montmort number (after Pierre Remond de Montmort). Notations for subfactorials in common use include !n, Dn, dn, or n¡.

For n > 0, the subfactorial !n equals the nearest integer to n!/e, where n! denotes the factorial of n and e is Euler's number.

The problem of counting derangements was first considered by Pierre Raymond de Montmort in his Essay d'analyse sur les jeux de hazard. in 1708; he solved it in 1713, as did Nicholas Bernoulli at about the same time.