Partitions with parts in a finite set

Author:
Melvyn B. Nathanson

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

Published electronically:
February 7, 2000

MathSciNet review:
1705753

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

**1.**P. Erdos and J. Lehner.

The distribution of the number of summands in the partitions of a positive integer.*Duke Math. J.*, 8:335-345, 1941. MR**3:69a****2.**S. Han, C. Kirfel, and M. B. Nathanson.

Linear forms in finite sets of integers.*Ramanujan J.*, 2:271-281, 1998. MR**99h:11011****3.**M. B. Nathanson.

Sums of finite sets of integers.*Amer. Math. Monthly*, 79:1010-1012, 1972. MR**46:3440****4.**E. Netto.*Lehrbuch der Combinatorik*.

Teubner, Leipzig, 1927.**5.**G. Pólya and G. Szegö.*Aufgaben und Lehrsätze aus der Analysis*.

Springer-Verlag, Berlin, 1925.

English translation:*Problems and Theorems in Analysis*, Springer-Verlag, New York, 1972. MR**49:8782**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
11P81,
05A17,
11B34

Retrieve articles in all journals with MSC (2000): 11P81, 05A17, 11B34

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:
https://doi.org/10.1090/S0002-9939-00-05606-9

Keywords:
Partition functions,
asymptotics of partitions,
additive number theory

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

Article copyright:
© Copyright 2000
American Mathematical Society