derangement

created by dem bones
(thing) by ariels (3.9 d) (print)   ?   (I like it!) Wed Aug 30 2000 at 10:52:48

A permutation with no fixed points. Any rotation is of this form, but the converse is not true for permutations on more than 3 elements.

The number of derangements of n elements is the integer closest to n!/e. This is the poster child for showing a use of the inclusion / exclusion principle (aka Poincare's method) -- see the node about counting fixed points of permutations.

(idea) by artemis entreri (11.8 mon) (print)   ?   (I like it!) Fri Dec 29 2000 at 1:51:28
To clarify ariels definition of derangement, with respect to combinatorics, it is a rearrangement of an ordered set of things so that no element is in its original position.

--back to combinatorics--
(definition) by Webster 1913 (print) Tue Dec 21 1999 at 23:00:38

De*range"ment (?), n. [Cf. F. d'erangement.]

The act of deranging or putting out of order, or the state of being deranged; disarrangement; disorder; confusion; especially, mental disorder; insanity.

Syn. -- Disorder; confusion; embarrassment; irregularity; disturbance; insanity; lunacy; madness; delirium; mania. See Insanity.

 

© Webster 1913.

Y'know, if you log in, you can write something here, or contact authors directly on the site. Create a New User if you don't already have an account.