Summary (taken from Zbl.):
The objective of this paper is to consider the combinatorial aspects of Ramanujan's congruences $p(5n+4)\equiv 0 (mod 5)$, $p(7n+5)\equiv 0 (mod 7)$ and $p(11n+6)\equiv 0 (mod 11)$. It starts with a brief survey of these congruences. Dyson's combinatorial interpretation of the first and second congruence in terms of rank is considered next. Dyson conjectured the existence of a crank for proof of the third. The author defines such a crank in terms of weighted count of certain vector partitions. It is shown that these results are related to identities from Ramanujan's `lost' notebook, the work of Atkin and Swinnerton-Dyer and the conjectures on mock theta functions stated by Andrews. Some combinatorial results related to the crank and rank differences are also proved. Finally the true crank discovered by Andrews and the author is defined in terms of ordinary partitions.