Bruce Chiarelli, Brigham Young University
Mathematical Sciences
A Gallai coloring of the complete graph on n vertices is an edge coloring such that no triangle has edges of three different colors.
We show that such a coloring solves the problem of finding partitions of the set of transpositions in the symmetric group S_n such that the corresponding sums in the complex group algebra CS_n commute. We do a similar thing for 3-cycles in S_n and give applications to the theory of S-rings.