Ricerc@Sapienza

Let Dh, Ek and Falpha be sets of size h; k; alpha respectively, with k less than or equal to
h. A permutation of the union of Dh, Ek and Falpha such that the elements of Dh
are not fixed and the elements of Ek cannot occupy a site originally
occupied by an object of the same type or by an object of Falpha will be
called a strongly widened derangement. We show a connection between
strongly widened derangements and generalized Laguerre polynomials
that provides a generalization, for integer values of alpha, of Even and Gillis (1976) different
from the one presented in Foata and Zeilberger (1988)..