Mathematical Proceedings of the Cambridge Philosophical Society

Table of Contents - 1976 - Volume 79, Issue 01  

Research Article

Derangements and Laguerre polynomials

S. Evena1 and J. Gillisa1

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

Abstract

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)