New Recurrence Relation for Partitions Into Distinct Parts

Denote by Q n the set of partitions of a positive integer n into distinct parts. For k ∈ N , denote by Q n,k the set of partitions of n into distinct parts whose least part is k + 1 and not equal to n . Let q ( n ) and q ( n, k ) be the number of elements in Q n and Q n,k , respectively. In this paper, several new recurrence relations for partitions into distinct parts are derived from the partition function q ( n, k ) .