The above discussion focused on additive partitions, but we can also consider multiplicative partitions, i. e. , the number of ways in which a positive integer n can be expressed as a product of integers …Template for partition theory product-sum generating functions combinatorics encoded in exponents, coefficients connected analysis to partitionsAs we have seen, the theory of multiplicative partitions hinges on a subject with a much longer historyâ€the theory of additive partitions, as it relates to the prime exponents.In number theory, a multiplicative partition or unordered factorization of an integer is a way of writing as a product of integers greater than 1, treating two products as equivalent if they differ only in the …