On Partial Sums in Cyclic Groups

TL;DR

This paper explores the problem of ordering elements in subsets of non-zero integers modulo n so that all partial sums are distinct, proposing a conjecture and providing partial results towards its proof.

Contribution

It introduces a conjecture on ordering elements in cyclic groups with distinct partial sums and offers partial theoretical results supporting this conjecture.

Findings

Proposed a conjecture on ordering elements with distinct partial sums.

Proved several partial results towards the conjecture.

Established foundational properties related to the problem.

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.