11-dissection and modulo 11 congruences properties for partition generating function

Abstract

In a recent paper, we give 13-dissection and some congruences for modulo 13 for the partition generating function � (1 − q r ) −1 by using a method of Kolberg. In this paper, by following similar course, we develop an algoritmic approach and give 11-dissection for the partition generating function � (1 − q r ) −1 . Then we re-obtain the congruences given by Atkin and Swinnerton-Dyer.