PIMS-UVic Distinguished Lecture: Brian Alspach

In 1961 B. Gordon defined a group to be sequenceable if its elements could be written in a sequence g_1,g_2,...,g_n such that the partial products g_1g_2...g_i are all distinct for i = 1 through n.  In 1974 Ringel asked for a sequencing of the non-identity elements so that successive pairs g_{i-1}g_i^{-1} are all distinct.  A group admitting this sequencing became known as an R-sequenceable group.  Friedlander, Gordon and Miller conjectured in 1978 that a finite abelian group is either sequenceable or R-sequenceable.  D. Kreher, A. Pastine and I have recently completed the proof of this conjecture.  I shall discuss this and place it in the context of Cayley digraphs which leads to a wide-open general problem.