Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Derangements and Laguerre polynomials

S. Evena1 and J. Gillisa1

a1 Department of applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel


Given a set consisting of n1, objects of type 1, n2 of type 2, …, nk of type k, we denote by S0305004100052154_inline1 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 S0305004100052154_inline2 in terms of Laguerre polynomials, and some of its implications are considered.

(Received December 04 1974)