derangement numbers

derangement numbers

[di′rānj·mənt ‚nəm·bərz]
(mathematics)
The numbers Dn, n = 1, 2, 3, …, giving the number of permutations of a set of n elements that carry no element of the set into itself.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Proof: Let [d.sup.k.sub.n] stand for the number of (n, k)-permutations; these are the rencontre numbers, which are related to the derangement numbers by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
A new generation tree for permutations, preserving the number of fixed points
Interestingly, this formula, which is a combination of factorials, can also be written as the same combination of an infinite family of other numbers, including the derangement numbers. We give a combinatorial interpretation of these families as the number of fixed point [lambda]-coloured permutations.
Enumeration of derangements with descents in prescribed positions
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