Sets in Abelian groups with distinct sums of pairs

JOURNAL OF NUMBER THEORY

卷:123

Article

Haanpaa, Harri ; Ostergard, Patric R. J.

关键词: additive base;    backtrack search;    difference set;    packing;   

DOI  :  10.1016/j.jnt.2006.06.007

来源: Elsevier

【 摘 要 】

A subset S = {s(l),..., 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. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free