Durfee Polynomial

Let $F(n)$ be a family of Partitions of $n$ and let $F(n,d)$ denote the set of Partitions in $F(n)$ with Durfee Square of size $d$. The Durfee polynomial of $F(n)$ is then defined as the polynomial

$$P_{F,n}= \sum \vert F(n,d)\vert y^d,$$

where $0\leq d \leq \sqrt{n}$.

See also Durfee Square, Partition

References

Canfield, E. R.; Corteel, S.; and Savage, C. D. ``Durfee Polynomials.'' Electronic J. Combinatorics 5, No. 1, R32, 1-21, 1998. http://www.combinatorics.org/Volume_5/v5i1toc.html#R32.