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On the sum and the difference of finite sets of integers

Published online by Cambridge University Press:  17 April 2009

Reinhard A. Razen
Reinhard A. Razen
Affiliation:
Institut für Mathematik und Mathematische Statistik, Montanuniversität Leoben, Leoben, Austria.
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Abstract

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Let A = {ai} be a finite set of integers and let p and m denote the cardinalities of A + A = {ai+aj} and A - A {ai–aj}, respectively. In the paper relations are established between p and m; in particular, if max {ai–ai-1} = 2 those sets are characterized for which p = m holds.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 15 , Issue 2 , October 1976 , pp. 245 - 251
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Macdonald, Sheila Oates and Street, Anne Penfold, “On Conway's conjecture for integer sets”, Bull. Austral. Math. Soc. 8 (1973), 355–358.CrossRefGoogle Scholar
[2]Spohn, William G. Jr., “On Conway's conjecture for integer sets”, Canad. Math. Bull. 14 (1971), 461–462.CrossRefGoogle Scholar