| 释义 |
DerangementA Permutation of  ordered objects in which none of the objects appears in its natural place. The functiongiving this quantity is the Subfactorial  , defined by
 | (1) |
 | (2) |
 is the usual Factorial and  is the Nint function. These are also called RencontresNumbers (named after rencontres solitaire), or Complete Permutations, orderangements. The number of derangements  of length satisfy the Recurrence Relations
 | (3) |
 | (4) |
 and  . The first few are 0, 1, 2, 9, 44, 265, 1854, ... (Sloane's A000166). This sequence cannot beexpressed as a fixed number of hypergeometric terms (Petkovsek et al. 1996, pp. 157-160).See also Married Couples Problem, Permutation, Root, Subfactorial
References
Aitken, A. C. Determinants and Matrices. Westport, CT: Greenwood Pub., p. 135, 1983.Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 46-47, 1987. Coolidge, J. L. An Introduction to Mathematical Probability. Oxford, England: Oxford University Press, p. 24, 1925. Courant, R. and Robbins, H. What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 115-116, 1996. de Montmort, P. R. Essai d'analyse sur les jeux de hasard. Paris, p. 132, 1713. Dickau, R. M. ``Derangements.''http://forum.swarthmore.edu/advanced/robertd/derangements.html. Durell, C. V. and Robson, A. Advanced Algebra. London, p. 459, 1937. Petkovsek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A. K. Peters, 1996. Roberts, F. S. Applied Combinatorics. Englewood Cliffs, NJ: Prentice-Hall, 1984. Ruskey, F. ``Information on Derangements.'' http://sue.csc.uvic.ca/~cos/inf/perm/Derangements.html. Sloane, N. J. A. SequenceA000166/M1937in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995. Stanley, R. P. Enumerative Combinatorics, Vol. 1. New York: Cambridge University Press, p. 67, 1986. Vardi, I. Computational Recreations in Mathematica. Reading, MA: Addison-Wesley, p. 123, 1991.
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