S-partitions

Abstract

This note reports on the number of s-partitions of a natural number n. In an s-partition of n 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 number of s-partitions presented by Bhatt [Inform. Process. Lett. 71 (1999) 141–148]. We will give a precise asymptotics for the number of such partitions for a given integer n.