Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-05-19T08:18:03.660Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

ANS90.Atkinson, M. D., Negro, A. and Santoro, N.. Sums of lexicographically ordered sets. Discrete Math., 80 (1990), 115–122.Google Scholar
B95.Bohman, T.. A sum packing problem of Erdős and the Conway-Guy sequence. Proc. A.M.S., 124 (1996), 3627–3636.CrossRefGoogle Scholar
CG68.Conway, J. H. and Guy, R. K.. Sets of natural numbers with distinct sums, Notice 654-32. Notices of the A.M.S., 15 (1968), 345.Google Scholar
CG69.Conway, J. H. and Guy, R. K.. Problem 209, Response 1. Colloquium Mathematicum. 20 (1969), 307.Google Scholar
E58.Erdős, P.. Problem 209. Colloquium Mathematicum, 5 (1958), 119.Google Scholar
G81.Guy, R. K.. Unsolved Problems in Number Theory (Springer-Verlag, 1981), Problem C8.Google Scholar
G82.Guy, R. K.. Sets of integers whose subsets have distinct sums. Annals of Discrete Mathematics 12: Theory and Practice of Combinatorics (North-Holland, 1982), 141–154.Google Scholar
L88.Lunnon, W. F.. Integer sets with distinct subset-sums. Mathematics of Computation, 50 (1988), 297–320.CrossRefGoogle Scholar