• 충청수학회지
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• 제21권2호
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• pp.223-230
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• 2008

In this paper, we present an upper bound of the reciprocal sums of generalized subset-sum-distinct sequences with respect to the first terms of the sequences. And we show the suggested upper bound is best possible. This is a kind of generalization of [1] which contains similar result for classical subset-sum-distinct sequences.

• 대한수학회논문집
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• 제17권2호
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• pp.215-220
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• 2002

Since P. Erdos introduced the concept of "subset-sum-distinctness", lots of mathematicians have been interested in a "dense" set having distinct subset sums. In this paper, we establish a couple of theorems on maximal subset-sun-distinct sequence with respect to the set inclusion.

• 대한수학회지
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• 제40권5호
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• pp.757-768
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• 2003

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.

• 대한수학회보
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• 제35권3호
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• pp.515-525
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• 1998

In this paper we obtain a "compactness" result that asserts the existence, in certain sets of sequences, of a sequence which has a maximal reciprocal sum. We derive this result from a much more general theorem which will be proved by introducing a metric into the set of sequences and using a topological argument.