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Asymptotic distribution of the number and size of parts in unequal partitions

Published online by Cambridge University Press:  17 April 2009

G. Szekeres
G. Szekeres
Affiliation:
School of Mathematics, University of New South Wales, Kensington, New South Wales, 2033, Australia.
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Abstract

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An asymptotic formula is derived for the number of partitions of a large positive integer n into r unequal positive integer parts and maximal summand k. The number of parts has a normal distribution about its maximum, the largest summand an extreme-value distribution. For unrestricted partitions the two distributions coincide and both are extreme-valued. The problem of joint distribution of unrestricted partitions with r parts and largest summand k remains unsolved.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 1 , August 1987 , pp. 89 - 97
Copyright
Copyright © Australian Mathematical Society 1987

References

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