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A Ramsey-type property in additive number theory

Published online by Cambridge University Press:  18 May 2009

S. A. Burr  and
P. Erdös
S. A. Burr
Affiliation:
City College, C.U.N.Y., New York NY 10031, U.S.A.
P. Erdös
Affiliation:
Hungarian Academy of Sciences
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Let A be a sequence of positive integers. Define P(A) to be the set of all integers representable as a sum of distinct terms of A. Note that if A contains a repeated value, we are free to use it as many times as it occurs in A. We call A complete if every sufficiently large positive integer is in P(A), and entirely complete if every positive integer is in P(A). Completeness properties have received considerable, if somewhat sporadic, attention over the years. See Chapter 6 of [3] for a survey.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 27 , October 1985 , pp. 5 - 10
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

REFERENCES

1.Burr, S. A., On the Completeness of Sequences of Perturbed Polynomial Values, Pacific J. Math. 85 (1979), 355–360.Google Scholar
2.Burr, S. A. and Erdos, P., Completeness Properties of Perturbed Sequences, J. Number Theory 13 (1981), 446–455.Google Scholar
3.Erdos, P. and Graham, R. L., Old and New Problems and Results in Combinatorial Number Theory, Monographic 28 (L'Enseignement Mathématique, 1980).Google Scholar
4.Graham, R. L., Rudiments of Ramsey Theory(American Mathematical Society, 1981).CrossRefGoogle Scholar
5.Graham, R. L., Rothschild, B. L., and Spencer, J. H., Ramsey Theory (Wiley, 1980).Google Scholar