Durfee polynomials
type: Item
instance of: scholarly article
title: Durfee polynomials
zbMATH Open document ID: 0896.05007
author: E. Rodney Canfield
author: Sylvie Corteel
author: Carla D. Savage
published in: The Electronic Journal of Combinatorics
publication date: 1998-07-06T00:00:00Z
full work available at URL: https://eudml.org/doc/119557
full work available at URL: v5i1r32.html
review text: 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.
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 05A20
Mathematics Subject Classification ID: 05A16
Mathematics Subject Classification ID: 11P81
zbMATH DE Number: 1171004
zbMATH Keywords: partitions
zbMATH Keywords: Durfee square
zbMATH Keywords: polynomials
zbMATH Keywords: bounds
zbMATH Keywords: sequences
reviewed by: R. Scurr
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1171004