Available in electronic format
Available in print format		 Mathematics of Computation
Journal of the American Mathematical Society
ISSN 1088-6842(e) ISSN 0025-5718(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Periodicity of the parity of a partition function related to making change

Author(s): Patrick Costello; Michael Osborne.
Journal: Math. Comp. 77 (2008), 1749-1754.
MSC (2000): Primary 11P83
Posted: February 13, 2008
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: The solutions to a change problem form restricted partitions. For one particular change problem, we look at the sequence representing the parity of these restricted partition values. It appears that the period of this sequence has not been studied. Through recurrences involving binomial coefficients, we find that the sequence has a period of $ 200$.

References:

1.
R. Blecksmith, J. Brillhart, and I. Gerst, Parity results for certain partition functions and identities similar to theta functions, Mathematics of Computation, 48 (177) (1987), pp. 29-38. MR 866096 (87k:11113)

2.
R. Graham, D. Knuth, and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, MA, 1990. MR 1397498 (97d:68003)

3.
M. D. Hirschhorn, On the residue $ \operatorname{mod}2$ and $ \operatorname{mod}4$ of $ p(n)$, Acta Arith., 38 (1980), pp. 105-109. MR 604226 (82d:10025)

4.
M. D. Hirschhorn, Parity results for certain partition functions, Ramanujan Journal, 4 (2000), pp. 129-135. MR 1782196 (2001i:11121)

5.
D. B. Lahiri, Some restricted partition functions: Congruences modulo 2, Trans. of the American Mathematical Society, 147 (1970), pp. 271-278. MR 0260694 (41:5318)

6.
P. A. MacMahon, Collected Papers, vol. 1, MIT Press, Cambridge, MA, 1978. MR 514405 (80k:01065)

7.
G. Polya, On picture-writing, American Mathematical Monthly, 63 (1956), pp. 689-697. MR 0081865 (18:458b)

Similar Articles:

Retrieve articles in Mathematics of Computation with MSC (2000): 11P83

Retrieve articles in all Journals with MSC (2000): 11P83

Additional Information:

Patrick Costello
Affiliation: Department of Mathematics and Statistics, Eastern Kentucky University, Richmond, Kentucky 40475-3102
Email: pat.costello@eku.edu

Michael Osborne
Affiliation: Department of Mathematics and Statistics, Eastern Kentucky University, Richmond, Kentucky 40475-3102

DOI: 10.1090/S0025-5718-08-02095-4
PII: S 0025-5718(08)02095-4
Keywords: Partitions, parity
Received by editor(s): August 2, 2007
Received by editor(s) in revised form: August 22, 2007
Posted: February 13, 2008
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google