S-partitions

Goh, William M. Y.; Hitczenko, Pawel; Shokoufandeh, Ali

S-partitions

Authors

Goh, William M. Y.

Hitczenko, Pawel

Shokoufandeh, Ali

Description

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.
5 pages