The Laws of Lambert and Beer relate the radiant, power in a beam of electromagnetic radiation, usually ordinary light, to the length of the path of the beam in an absorbing medium and to the concentration of the absorbing species, respectively. The laws are normally combined in the relation A = -logic tt = abc -to where A = absorbance, formerly called the optical density, P = radiant power, formerly called the intensity, a = absorptivity, formerly called the extinction coefficient, b = length of the beam in the absorbing medium, c = concentration of the absorbing species.

Given a positiver integer m and an ordered k -tuple c = ( c 1 , ··· , c k ) of not necessarily distinct positive integers, then any ordered k -tuple s = ( s 1 , ··· , s k ) of nonnegative integers such that m = ∑ k i -1 s i c i is said to be a partition of m restricted to c . Let P c ( m ) denote the number of distinct partitions of m restricted to c . The subroutine COUNT , when given a k -tuple c and an integer n , computes an array of the values of P c ( m ) for m = 1 to n . Many combinatorial enumeration problems may be expressed in terms of the numbers P c ( m ). We mention two below.

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