Durfee polynomials
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 \(d\). This paper investigates the sequences \(\{F(n,d)\}\) for fixed \(n\), by examining polynomials having \(F(n,d)\) as the coefficients. The work of the paper is motivated by empirical evidence which suggests that for several families \(F\), all roots of the Durfee polynomial are real. Such a result implies that the corresponding sequence of coefficients \(\{| F(n,d)|\}\) is log-concave and unimodular.
scientific article; zbMATH DE number 1171004