A well-known question in combinatorial group theory, going back to a conjecture of Graham from 1971, asks if given a subset S of some group (G,+), it is possible to order S as s_1, s_2,..., s_t so that the partial sums s_1 + s_2 + ... + s_j are all distinct for each j < t. We discuss recent progress on this question based on a synergy between ideas from additive combinatorics and graph theory.
Based on joint work with Benjamin Bedert, Alp Muyesser, Noah Kravitz, and Richard Montgomery.
