ABSTRACT
The number (n)
k
, of k-permutations of n, and the number
n
k
, of k-
combinations of n, constitute particular cases of the factorial and the bino-
mial of a real number x of order k, respectively. The concept of a factorial is
as important as the concept of a power. In the calculus of nite dierences,
a major subject of discrete mathematics, factorials occupy the same central
position as the powers in the innitesimal calculus. The nite dierences of
factorials possess many of the nice properties of the derivatives of powers.
The binomial (coeÆcient), closely related to factorial, is of equal impor-
tance. In discrete probability theory and in theoretical computer science,
which concern nite dierences and sums of functions, the expansion into
factorial series is more advantageous than the expansion into power series.
The multinomial (coeÆcient) is a multivariate extension of the binomial
(coeÆcient).
