Invisible permutations and rook placements on a Ferrers board
type: Item
instance of: scholarly article
title: Invisible permutations and rook placements on a Ferrers board
zbMATH Open document ID: 0824.05062
DOI: 10.1016/0012-365X(93)00128-R
author: Kequan Ding
published in: Discrete Mathematics
publication date: 1995-10-26T00:00:00Z
review text: We study non-attacking rook placements on a Ferrers board by extending them to certain permutation matrices, called invisible permutations. By introducing a length function on rook placements, we define a rook length polynomial \(\text{RL}_ k(\lambda, q)\) for a given number \(k\) of rooks and a Ferrers board \(F_ \lambda\). We prove that \(\text{R}_ k(\lambda, q)= q^{C_{\lambda,k}} \text{RL}_ k(\lambda, q)\), where \(\text{R}_ k(\lambda, q)\) is a Garsia-Remmel polynomial. Further, we give explicit formulae for Garsia-Remmel polynomials and rook length polynomials.
reviewed by: Kequan Ding
Mathematics Subject Classification ID: 05E35
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 773905
zbMATH Keywords: rook placements
zbMATH Keywords: Ferrers board
zbMATH Keywords: invisible permutations
zbMATH Keywords: rook length polynomial
zbMATH Keywords: Garsia-Remmel polynomial
zbMATH Keywords: length
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 773905