On a Partition Function of Richard Stanley
Copyright policy )On a Partition Function of Richard Stanley
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 $t(n)$.
- Pennsylvania State University United States
partition identities, Combinatorial aspects of partitions of integers, generating function, Exact enumeration problems, generating functions, Elementary theory of partitions, Combinatorial identities, bijective combinatorics
partition identities, Combinatorial aspects of partitions of integers, generating function, Exact enumeration problems, generating functions, Elementary theory of partitions, Combinatorial identities, bijective combinatorics
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