Partitions into large unequal parts from a general sequence

Abstract

An asymptotic estimate is obtained for the number of partitions of the positive integer n into unequal parts coming from a sequence u, with each part greater than m, under suitable conditions on the sequence u. The estimate holds uniformly with respect to integers m such that $0\le m \le n^{1-\delta }$, as $n\to\infty $, where $\delta $ is a given real number, such that $0<\delta < 1$.