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On a conjecture of Guinand for the plane partition function

Published online by Cambridge University Press:  20 January 2009

George E. Andrews
George E. Andrews
Affiliation:
Pennsylvania State University, University Park, Pennsylvania 16802
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In (1; p. 38), A. P. Guinand discusses the plane partition function q(n). He observes that q(3), q(6), q(9), q(15), q(18), q(21), and q(24) are respectively 6, 48, 282, 1479, 6879, 29601, 118794, and 451194. As all these are multiples of 3 he suggests the conjecture that q(3n) ≡ 0 (mod 3) for all positive integers n.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 17 , Issue 3 , June 1971 , pp. 275 - 276
Copyright
Copyright © Edinburgh Mathematical Society 1971

References

REFERENCES

(1)Guinand, A. P., Report of the Research Committee on the Summer Research Institutes (Canadian Math. Congress, 1969).Google Scholar
(2)Macmahon, P. A., Combinatory Analysis, vol. 2 (Cambridge University Press, Cambridge, 1916).Google Scholar
(3)Wright, E. M., Rotatable partitions, J. London Math. Soc., 43 (1968), 501–505.CrossRefGoogle Scholar