Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A GENERALIZATION OF A SUBSET-SUM-DISTINCT SEQUENCE

  • Bae, Jae-Gug (Department of Applied Mathematics Korea Maritime University) ;
  • Choi, Sung-Jin (Department of Applied Mathematics Korea Maritime University)
  • Published : 2003.09.01
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Abstract

In 1967, as an answer to the question of P. Erdos on a set of integers having distinct subset sums, J. Conway and R. Guy constructed an interesting sequence of sets of integers. They conjectured that these sets have distinct subset sums and that they are close to the best possible with respect to the largest element. About 30 years later (in 1996), T. Bohman could prove that sets from the Conway-Guy sequence actually have distinct subset sums. In this paper, we generalize the concept of subset-sum-distinctness to k-SSD, the k-fold version. The classical subset-sum-distinct sets would be 1-SSD in our definition. We prove that similarly derived sequences as the Conway-Guy sequence are k-SSD.

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References

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