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Introduction. The problem of determining the formula for $P_S\left(n\right)$, the number of partitions of an integer into elements of a finite set S, that is, the number of solutions in non-negative integers, $h_{s₁},...,h_{s_k}$, of the equation hs₁ s₁ + ... + hsk sk = n, was solved in the nineteenth century (see Sylvester [4] and Glaisher [3] for detailed accounts). The solution is the coefficient of$xⁿin$[(1-xs₁)... (1-xsk)]-1, expressions for which they derived. Wright [5] indicated a simpler method by which to find part of the solution...