On congruence properties of $p(n,m)$
HTML articles powered by AMS MathViewer
- by Brandt Kronholm PDF
- Proc. Amer. Math. Soc. 133 (2005), 2891-2895 Request permission
Abstract:
In the late 19th century, Sylvester and Cayley investigated the properties of the partition function $p(n,m)$. This function enumerates the partitions of a non-negative integer $n$ into exactly $m$ parts. Here we investigate the congruence properties of such functions and we obtain several infinite classes of Ramanujan-type congruences.References
- George E. Andrews, Partitions: at the interface of $q$-series and modular forms, Ramanujan J. 7 (2003), no. 1-3, 385–400. Rankin memorial issues. MR 2035813, DOI 10.1023/A:1026224002193
- A. O. L. Atkin, Proof of a conjecture of Ramanujan, Glasgow Math. J. 8 (1967), 14–32. MR 205958, DOI 10.1017/S0017089500000045
- H. Gupta, E. E. Gwyther and J. C. P. Miller, Tables of Partitions, Royal Soc. Math. Tables, Vol. 4, Cambridge University Press, Cambridge, 1958.
- Ken Ono, Distribution of the partition function modulo $m$, Ann. of Math. (2) 151 (2000), no. 1, 293–307. MR 1745012, DOI 10.2307/121118
- S. Ramanujan, Collected Papers, Cambridge University Press, London, 1927; reprinted: A. M. S. Chelsea, 2000 with new preface and extensive commentary by B. Berndt.
- G. N. Watson, Ramanujan’s Vermutung über Zerfällungsanzahlen, J. reine und angew. Math 179 (1938), 97-128.
Additional Information
- Brandt Kronholm
- Affiliation: Department of Mathematics, Penn State University, University Park, Pennsylvania 16802
- Address at time of publication: Department of Mathematics, University at Albany, Albany, New York 12222
- MR Author ID: 766642
- Email: kronholm@math.psu.edu
- Received by editor(s): June 9, 2004
- Published electronically: April 25, 2005
- Communicated by: David E. Rohrlich
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 2891-2895
- MSC (2000): Primary 05A17, 11P83
- DOI: https://doi.org/10.1090/S0002-9939-05-07972-4
- MathSciNet review: 2159766