## PIMS-UVic Distinguished Lecture: Brian Alspach

- Date: 05/09/2016
- Time: 14:30

*University of Newcastle*

University of Victoria

Sequenceable groups and generalizations

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.

2:30 pm (refreshments at 2:00 pm)

Location: University of Victoria, David Strong Building, room C126