Brandt KronholmAffiliation: Juniata College Email: kronholm@juniata.edu Title Of Talk: Towards a Complete Characterization of New Ramanujan Congruence Properties of the Restricted Partition Function $p(n,m)$. Abstract: In this presentation we will discuss an intriguing extension of a previous result regarding $p(n,m)$, the restricted partition function that enumerates the number of partitions of $n$ into exactly $m$ parts. This extension reveals further symmetries of the generating function for $p(n,m)$ and may allow us to gain a better understanding of these Ramanujan-like congruences. Moreover, this extension agrees with the Hardy-Ramanujan-Rademacher formula for $p(n)$ when $n$ is negative, namely, $p(n)=0$.
Last update made Tue Sep 11 13:25:29 EDT 2012.
|