Séminaire Lotharingien de Combinatoire, B08c (1984), 9 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1984, 229/S-08, p. 17-25.]

Dominique Foata and Doron Zeilberger

Weighted Derangements and Laguerre Polynomials

Abstract. The integral of a product of finitely many generalized Laguerre polynomials with respect to their weight function is expressed as the generating polynomial for so-called (a,b,...,d)-derangements by their numbers of cycles. The positivity of the integral is a consequence of this combinatorial interpretation.

The present paper has been completed and updated to become:
Dominique Foata and Doron Zeilberger, Laguerre polynomials, weighted derangements and positivity, SIAM J. Discrete Math., vol. 1, 1988, p. 425--433.

The following versions are available: