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A generalization of a subset-sum-distinct sequence
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Abstract
In 1967, as an answer to the question of P. Erd"os on aset of integers having distinct subset sums, J. Conway and R. Guyconstructed an interesting sequence of sets of integers. Theyconjectured that these sets have distinct subset sums and thatthey are close to the best possible with respect to the largestelement. About 30 years later (in 1996), T. Bohman could provethat sets from the Conway-Guy sequence actually have distinctsubset sums. In this paper, we generalize the concept ofsubset-sum-distinctness to bb k-SSD, the bb k-fold version.The classical subset-sum-distinct sets would be 1-SSD in ourdefinition. We prove that similarly derived sequences as theConway-Guy sequence are bb k-SSD.
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