Mathematical Research Letters
Volume 17 (2010)
Rank-Crank type PDE’s and non-holomorphic Jacobi forms
Pages: 589 – 600
In this paper we show how Rank-Crank type PDE’s (first found by Atkin and Garvan) occur naturally in the framework of non-holomorphic Jacobiforms and find an infinite family of such differential equations. As an application we show an infinite family of congruences for odd Durfee symbols, a partition statistic introduced by George Andrews.