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On Conway's conjecture for integer sets

Published online by Cambridge University Press:  17 April 2009

Sheila Oates Macdonald  and
Anne Penfold Street
Sheila Oates Macdonald
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland.
Anne Penfold Street
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland.
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Abstract

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Let A = {ai} be a finite set of integers and let p, m denote the orders of A + A = {ai+aj} and A – A = {ai–aj} respectively. J.H. Conway conjectured that p ≤ m always and that p = m only if A is symmetric about 0. This conjecture has since been disproved; here we make several other observations on the values of p and m.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 8 , Issue 3 , June 1973 , pp. 355 - 358
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Conway, J.H., Problem 7 of Section VI of H.T. Croft's Research problems (mimeographed notes, Cambridge, August 1967).Google Scholar
[2]Marica, John, “On a conjecture of Conway”, Canad. Math. Bull. 12 (1969), 233–234.CrossRefGoogle Scholar
[3]Spohn, William G. Jr, “On Conway's conjecture for integer sets”, Canad. Math. Bull. 14 (1971), 461–462.CrossRefGoogle Scholar
[4]Stein, S.K., “The cardinalities of A + A and A − A”, Canad. Math. Bull. (to appear).Google Scholar