Rainbow Arithmetic Progressions I : Search Algorithm

At Iowa State, we tried an experiment this year to have a Discrete Mathematics Working Seminar where the group that normally meets for a research talk stays for an extra hour a week to work on a research problem. The goal was to break into smaller groups, but we ended up staying as one giant mass of mathematicians, including 5 faculty, a lecturer, and 6 graduate students. We recently posted the result to the arXiv:

S. Butler, C. Erickson, L. Hogben, K. Hogenson, L. Kramer, R. L. Kramer, J. C.-H. Lin, R. R. Martin, D. Stolee, N. Warnberg, and M. Young, Rainbow arithmetic progressions, arXiv:1404.7232 [math.CO]

Today, we will discuss the backtrack-search that was used to gather initial data on this problem. Since the paper features proofs as its main feature, not all of the algorithmic details were discussed (but enough were that anyone could figure out the rest). Here, I’ll flesh out as much detail as I can. In a later post, I will comment on the experimental collaboration.