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. We de ne the Durfee polynomial of F(n) to be the polynomial PF n = P jF(n d)jyd, where 0 d bpnc: The work in this paper is motivated by empirical evidence which suggests that for several families F, all roots of the Durfee polynomial are real. Such a result would imply that the corresponding sequence of coe cients fjF(n d)jg is logconcave and unimodal and that, over all partitions in F(n) for xed n, the Research supported by National Science Foundation Grant DMS9302505 ySupported in part by National Science Foundation Grants No. DMS 9302505 and DMS 9622772 1 

• Type: Journal
• Year: 1998
• Where: COMBINATORICS
• Authors: E. Rodney Canfield, Sylvie Corteel, Carla D. Savage
• Keywords: COMBINATORICS 1998, Durfee Polynomial, Durfee Square, Polynomial Pf