Math 2.0

Combinatorics Theorem

The derangement numbers count derangements

Builds on DerangementNumber of derangements

Statement

Let XX be a finite set with ∣X∣=n|X| = n. Then the number of derangements of XX is the derangement number DnD_n of the node number of derangements.

Remarks

The proof checks the recursion Dn+2=(n+1)(Dn+Dn+1)D_{n+2} = (n + 1)(D_n + D_{n+1}), as in the node recurrence for derangements. For n=4n = 4 there are 99 derangements among the 2424 permutations.

Reading path

To understand this page from the ground up, read these 4 pages in order. The foundations come first.

Show the path as a graph
Number of derangements, definition, no evidence levelNumber of derangementsdefinitionPermutation, definition, no evidence levelPermutationdefinitionDerangement, definition, no evidence levelDerangementdefinitionThe derangement numbers count derangements, statement, no evidence levelThe derangement numbe…statement
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Number of derangements definition
  2. Permutation definition
  3. Derangement definition
  4. The derangement numbers count derangements statement

Further reading

  1. Web https://en.wikipedia.org/wiki/Derangement, Counting derangements
About this page
Tag045ENVCCZV
URIm2://045ENVCCZV
Kindstatement, theorem
WritingW0 stub
MSC05A05
StatusThis copy of the site has no build data. Run m2 status 045ENVCCZV.
UsesDerangement, Number of derangements

Markdown · JSON · Edit on GitHub

What this page needs for W1

  • an inventory row: the row of the inventory that the node accounts for (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

What links here

No page links to this page yet.