This site is supported by donations to The OEIS Foundation.
Derangements
From OeisWiki
Derangements are permutations with no rencontre (“rencontre” is french for “encounter”), i.e. no fixed-point.
Example
The 6 permutations of (1, 2, 3) are, in lexicographic order: {(1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1)} among which
- {(1, 2, 3)} (obviously) have 3 rencontres (fixed-points);
- ∅ (obviously) have 2 rencontres;
- {(1, 3, 2), (2, 1, 3), (3, 2, 1)} have 1 rencontre;
- {(2, 3, 1), (3, 1, 2)} have 0 rencontre.
The 2 derangements of (1, 2, 3) are thus {(2, 3, 1), (3, 1, 2)}.
See also
- Derangement numbers (number of permutations with no rencontre, i.e. no fixed-point)
- Number of permutations with k rencontres
- Arrangements