An efficient representation of partitions of integers

Abstract

We introduce a data structure for representing a partition of an integer n, which uses O√n bits of space. This is constant multiple of the information theoretic lower bound. Three types of operations accessp, boundp, prefixsump are supported in constant time by using the notion of conjugate of a partition. In order to construct this data structure, we also construct a data structure for representing a monotonic sequence, which supports the same operations in constant time and uses (Formula Presented) bits of space for any positive constant δ. (n is the number of terms, and u denotes the size of the universe.).