Math 2.0

Combinatorics Definition

Derangement

Builds on Permutation

Definition

Let XX be a set. A derangement of XX is a permutation σ\sigma of XX such that σ(x)≠x\sigma(x) \neq x for all x∈Xx \in X. In other words, it is a permutation with no fixed point.

Remarks

The derangements of {1,2,3}\{1, 2, 3\} are 231231 and 312312 in one-line notation. The number of derangements of an nn-element set is written DnD_n or !n!n.

Reading path

To understand this page from the ground up, read these 2 pages in order. The foundations come first.

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Permutation, definition, no evidence levelPermutationdefinitionDerangement, definition, no evidence levelDerangementdefinition
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  1. Permutation definition
  2. Derangement definition

Where this leads

3 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Derangement, lead section
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