Self-Similarity of the 11-Regular Partition Function

Abstract

The partition function counts the number of ways a positive integer can be written as the sum of a non-increasing sequence of positive integers. These sums are known as partitions. The famous mathematician Srinivasa Ramanujan proved the partition function has beautiful divisibility properties. We will consider the k-regular partition function, which counts the partitions where no part is divisible by k. Results on the arithmetic of k-regular partition functions have been proven by several authors. In this paper we establish self-similarity results for the 11-regular partition function.