Partitions with parts in a finite set
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- by Melvyn B. Nathanson PDF
- Proc. Amer. Math. Soc. 128 (2000), 1269-1273 Request permission
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 \[ p_A(n) = \left (\frac {1}{\prod _{a\in A}a}\right ) \frac {n^{k-1}}{(k-1)!} + O\left ( n^{k-2}\right ). \]References
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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
- Received by editor(s): June 5, 1998
- Published electronically: 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 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1269-1273
- MSC (2000): Primary 11P81; Secondary 05A17, 11B34
- DOI: https://doi.org/10.1090/S0002-9939-00-05606-9
- MathSciNet review: 1705753