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Bigger and better subset-sum-distinct sets

Part of: Sequences and sets

Published online by Cambridge University Press:  26 February 2010

Roy Maltby
Roy Maltby
Affiliation:
Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4. e-mail: rmaltby@ucalgary.ca
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Abstract

Call a set of natural numbers subset-sum-distinct (or SSD) if all pairwise distinct subsets have unequal sums. One wants to construct SSD sets in which the largest element is as small as possible. Given any SSD set, it is easy to construct an SSD set with one more element in which the biggest element is exactly double the biggest element in the original set. For any SSD set, we construct another SSD set with k more elements whose largest element is less than 2k times the largest element in the original set. This claim has been made previously for a different construction, but we show that that claim is false.

MSC classification

Secondary: 11B75: Other combinatorial number theory

Information

Type
Research Article
Information
Mathematika , Volume 44 , Issue 1 , June 1997 , pp. 56 - 60
Copyright
Copyright © University College London 1997

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