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Partitions with parts in a finite set

Author(s): Melvyn B. Nathanson
Journal: Proc. Amer. Math. Soc. 128 (2000), 1269-1273.
MSC (2000): Primary 11P81; Secondary 05A17, 11B34
Posted: February 7, 2000
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Abstract:

Let $A$ be a nonempty finite set of relatively prime positive integers, and let $p_A(n)$ denote the number of partitions of $n$ with parts in $A$. An elementary arithmetic argument is used to prove the asymptotic formula

\begin{displaymath}p_A(n) = \left(\frac{1}{\prod_{a\in A}a}\right) \frac{n^{k-1}}{(k-1)!} + O\left( n^{k-2}\right). \end{displaymath}

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Additional Information:

Melvyn B. Nathanson
Affiliation: Department of Mathematics, Lehman College (CUNY), Bronx, New York 10468
Address at time of publication: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
Email: nathansn@alpha.lehman.cuny.edu, nathansn@ias.edu

DOI: 10.1090/S0002-9939-00-05606-9
PII: S 0002-9939(00)05606-9
Keywords: Partition functions, asymptotics of partitions, additive number theory
Received by editor(s): June 5, 1998
Posted: February 7, 2000
Additional Notes: This work was supported in part by grants from the PSC--CUNY Research Award Program and the NSA Mathematical Sciences Program.
Communicated by: David E. Rohrlich
Copyright of article: Copyright 2000, American Mathematical Society

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