A sum packing problem of Erd\H{o}s and the ConwayGuy sequence
Author:
Tom Bohman
Journal:
Proc. Amer. Math. Soc. 124 (1996), 36273636
MSC (1991):
Primary 11P99; Secondary 05D10
MathSciNet review:
1363448
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Abstract: A set of positive integers has distinct subset sums if the set has distinct elements. Let In 1931 Paul Erd\H{o}s conjectured that for some constant . In 1967 John Conway and Richard 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 largest element). We prove that sets from this sequence have distinct subset sums. We also present some variations of this construction that give microscopic improvements in the best known upper bound on .
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Additional Information
Tom Bohman
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Address at time of publication:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email:
bohman@math.rutgers.edu
DOI:
http://dx.doi.org/10.1090/S0002993996036532
PII:
S 00029939(96)036532
Received by editor(s):
June 6, 1995
Communicated by:
Jeffry N. Kahn
Article copyright:
© Copyright 1996 American Mathematical Society
