Sets In Abelian Groups With Distinct Sums Of Pairs

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. In this article, bounds for s(G) are developed and v(k) is determined for k 15 by computing s(G) for Abelian groups of order up to 183 using exhaustive backtrack search with isomorph rejection. © 2006 Elsevier Inc. All rights reserved.

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