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Sets in Abelian groups with distinct sums of pairs

✍ Scribed by Harri Haanpää; Patric R.J. Östergård

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
141 KB
Volume
123
Category
Article
ISSN
0022-314X

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✦ Synopsis

A subset S = {s 1 , . . . , s k } of an Abelian group G is called an S t -set of size k if all sums of t different elements in S are distinct. Let s(G) denote the cardinality of the largest S 2 -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.

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