On Partial Sums in Cyclic Groups

Dan S. Archdeacon1, Jeffrey H. Dinitz1, Amelia Mattern2, Douglas R. Stinson2
1Department of Mathematics and Statistics, University of Vermont, Burlington, VT 05405 U.S.A.
2David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

Abstract

We are interested in ordering the elements of a subset \( A \) of the non-zero integers modulo \( n \) in such a way that all the partial sums are distinct. We conjecture that this can always be done, and we prove various partial results about this problem.