S-partitions

Abstract

This note reports on the number of s-partitions of a natural number n. In an s-partition each cell has the form $2^k-1$ for some integer k. Such partitions have potential applications in cryptography, specifically in distributed computations of the form $a^n$ mod m. The main contribution of this paper is a correction to the upper bound on the number of s-partitions presented by Bhatt. We will give a precise asymptotics for the number of such partitions for a given integer n.