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Derangements and Laguerre polynomials

  • S. Even (a1) and J. Gillis (a1)


Given a set consisting of n1, objects of type 1, n2 of type 2, …, nk of type k, we denote by the number of possible derangements of the set i.e. permutations in which no object occupies a site originally occupied by an object of the same type. A formula is found for in terms of Laguerre polynomials, and some of its implications are considered.



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(1)Erdélyi, A. et al. Higher transcendental functions, vol. 1 (New York; McGraw-Hill, 1953).
(2)Erdélyi, A. et al. Higher transcendental functions, vol. 2 (New York; McGraw-Hill, 1953).
(3)Gillis, J. and Weiss, G.Products of Laguerre Polynomials. Math. Comp. 14 (1960), 60.
(4)Watson, G. N.A note on the polynomials of Hermite and Laguerre. J. London Math. Soc. 13 (1938), 29.


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