Sets in Abelian Groups with Distinct Sums of Pairs

@inproceedings{Haanp2002SetsIA,
title={Sets in Abelian Groups with Distinct Sums of Pairs},
author={Harri Haanp{\"a}{\"a} and Patric R. J. {\"O}sterg{\aa}rd},
year={2002}
}

A subset S = {s1, . . . , sk} of an Abelian group G is called an St-set of size k if all sums of t different elements in S are distinct. Let s(G) denote the cardinality of the largest S2-set in G. Let v(k) denote the order of the smallest Abelian group for which s(G) ≥ k. We develop bounds for s(G), and we determine v(k) for k ≤ 15 by determining s(G) for Abelian groups of order up to 183 using exhaustive backtrack search with isomorph rejection.