A Construction for Sets of Integers with Distinct Subset Sums

@article{Bohman1998ACF,
  title={A Construction for Sets of Integers with Distinct Subset Sums},
  author={Tom Bohman},
  journal={Electr. J. Comb.},
  year={1998},
  volume={5}
}
A set S of positive integers has distinct subset sums if there are 2|S| distinct elements of the set {∑ x∈X x : X ⊂ S } . Let f(n) = min{max S : |S| = n and S has distinct subset sums}. Erdős conjectured f(n) ≥ c2n for some constant c. We give a construction that yields f(n) < 0.22002 · 2n for n sufficiently large. This now stands as the best known upper bound on f(n). 

From This Paper

Topics from this paper.

Citations

Publications citing this paper.
Showing 1-3 of 3 extracted citations

References

Publications referenced by this paper.
Showing 1-8 of 8 references

The Conway–Guy sequence and a sum packing problem of Erdős

T. Bohman
Proceedings Amer. Math. Soc., • 1996

Unsolved problems in elementary number theory

Journal of Automated Reasoning • 1991
View 2 Excerpts

Sets of integers whose subsets have distinct sums

R. K. Guy
Ann . Discrete Math . • 1982

Sets of integers whose subsets have distinct sums, Ann

R. K. Guy
Discrete Math., • 1982

Sets of natural numbers with distinct subset sums

CG J.H. Conway, R. K. Guy
Notices Amer. Math. Soc., • 1968

Problems and results from additive number theory, Colloq

P. Erdős
Théorie des nombres, • 1955

Similar Papers

Loading similar papers…