An open problem in abstract mathematics is finding the lengths and multiplicities of the disjoint cycle decomposition (DCD) of the composition of permutations. Using toplogical arguments, it has been proven that the composition of N cycles can be decomposed into at most N cycles of distinct lengths. However, the topological approach does not yield the actual formulas for the lengths and multiplicites of the resulting DCD's. A completely different approach is required to arrive at the formulas.

To this end, we have written HPC code to compute the DCD of the composition of cycles. This code has evolved over the last two semesters in various ways, each version allowing us to compute DCD's of larger sets of permutation compositions, while at the same time reducing the space required to store them. Our current phase of computational research involves writing HPC code to analyze the large data sets we have created. Of great important is the ability to test conjectures against the data sets. We will detail our experiences and results found thus far and our future goals.

Presenter(s)

Karl Frinkle | Mike Morris | Keith Pearce | Jameson Carpenter | Jacob Graham | Nicholas Gauthier | Nathan Naylor