S-partitions

الأصل · EN

This note reports on the number of s-partitions of a natural number n. In an s-partition each cell has the form 2ᵏ-1 for some integer k. Such partitions have potential applications in cryptography, specifically in distributed computations of the form aⁿ 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.