On a partition function of Richard Stanley

Abstract

In this paper, we examine partitions π classified according to the number r(π) of odd parts in π and s(π) the number of odd parts in π′, the conjugate of π. The generating function for such partitions is obtained when the parts of π are all ≦ N. From this a variety of corollaries follow including a Ramanujan type congruence for Stanley's partition function t(n).