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Laguerre polynomials and derangements

Published online by Cambridge University Press:  24 October 2008

D. M. Jackson
D. M. Jackson
Affiliation:
University of Waterloo, Ontario
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Extract

Consider a sequence of n = n1 + … + nk objects of k distinct types such that there are ni objects of type i, i = 1, …, k. A derangement of this sequence is a permutation such that no object is in a position which was occupied by an object of the same type. To fix ideas, we may suppose that the sequence is initially ordered so that objects of type i precede those of type i + 1, i = 1, …, k – 1. Let Pn. denote the number of derangements of this sequence, where n = (n1, …, nk).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 2 , September 1976 , pp. 213 - 214
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

REFERENCES

(1)Even, S. and Gillis, J.Derangements and Laguerre polynomials. Math. Proc. Cambridge Philos. Soc. 79 (1976), 135–143.CrossRefGoogle Scholar
(2)Riordan, J.An introduction to combinatorial analysis (New York, Wiley, 1958).Google Scholar