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On some new types of partitions associated with generalized ferrers graphs

Published online by Cambridge University Press:  24 October 2008

F. C. Auluck
F. C. Auluck
Affiliation:
Delhi UniversityIndia
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Extract

1. In this paper we find generating functions and asymptotic expressions for the number of partitions of a positive integer n into two sets of positive integers satisfying the conditions

The set ‘b’ can be empty. Such partitions are considered by Temperley (1) in a forth-coming paper on the roughness of crystal surfaces. We shall consider them in more detail and under different sets of conditions on the a's and b's.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 4 , October 1951 , pp. 679 - 686
Copyright
Copyright © Cambridge Philosophical Society 1951

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References

REFERENCES

(1)Temperley, H. N. V. Statistical mechanics and the partitions of numbers. II. The form of crystals. (To be published shortly.)Google Scholar
(2)MacMahon, P. A.Combinatory analysis 2 (Cambridge, 1916), 79.Google Scholar
(3)Tannery, J. and Molk, J.Eléments de la théorie des founctions elliptiques, 3 (Paris, 1898), 135.Google Scholar