This paper introduces an algorithm for multiplying symmetric polynomials represented by partitions, sidestepping the need for algebraic symbol manipulation. Such Po´lya enumeration problems as the counting of chemical isomers is a use for the algorithm. By eliminating repetitive identification and collection of common terms and reducing storage requirements, this approach proves useful in rapidly expanding the figure counting series. Because the repetitive identification and collection of common terms are eliminated and storage requirements reduced. This algorithm offers a practical solution for efficiently expanding figure counting series in Po´lya enumeration problems, particularly beneficial for object sets with higher degrees of symmetry.
This algorithmic paper, published in ACM Transactions on Mathematical Software, contributes to the journal's focus on numerical algorithms and software tools. By introducing an algorithm for multiplying symmetric polynomials, it aligns with the journal's aim of providing effective methods for mathematical computation.