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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Computing the integer partition function


Authors: Neil Calkin, Jimena Davis, Kevin James, Elizabeth Perez and Charles Swannack
Journal: Math. Comp. 76 (2007), 1619-1638
MSC (2000): Primary 05A17; Secondary 11P81, 11P83
Published electronically: February 28, 2007
MathSciNet review: 2299791
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Abstract: In this paper we discuss efficient algorithms for computing the values of the partition function and implement these algorithms in order to conduct a numerical study of some conjectures related to the partition function. We present the distribution of $ p(N)$ for $ N \le 10^9$ for primes up to $ 103$ and small powers of $ 2$ and $ 3$.


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Additional Information

Neil Calkin
Affiliation: Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634-0975
Email: calkin@clemson.edu

Jimena Davis
Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695
Email: jldavis9@unity.ncsu.edu

Kevin James
Affiliation: Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634-0975
Email: kevja@clemson.edu

Elizabeth Perez
Affiliation: Applied Mathematics and Statistics, The Johns Hopkins University, G.W.C. Whiting School of Engineering, 302 Whitehead Hall, 3400 North Charles Street, Baltimore, Maryland 21218-2682
Email: eaperez@ams.jhu.edu

Charles Swannack
Affiliation: Department of Electrical and Computer Engineering, Clemson University, Clemson, South Carolina 29634
Address at time of publication: Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: swannack@mit.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-07-01966-7
PII: S 0025-5718(07)01966-7
Keywords: Partition function, discrete fast Fourier transforms
Received by editor(s): March 11, 2005
Received by editor(s) in revised form: July 10, 2006
Published electronically: February 28, 2007
Additional Notes: The authors were partially supported by NSF grant DMS-0139569
The third author was partially supported by NSF grant DMS-0090117
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.