Matrix relationships for partition functions (Q1364072)

We propose a multiplicative decomposition of a vector whose elements are partition function values into upper triangular Toeplitz matrices. The resulting expression is a natural consequence of ideas that are traceable to H. Gupta. It is of interest for processing on parallel computing systems with complex data structures. We show the relationship of the decomposition with the generating function of \(p(n)\). The computational complexity of the expression is analyzed. We also consider the possibility of reducing computational complexity.