On a Partition Function of Richard Stanley

George E. Andrews

Abstract


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


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