Determinants in plane partition enumeration
type: Item
instance of: scholarly article
title: Determinants in plane partition enumeration
zbMATH Open document ID: 0908.05007
author: George E. Andrews
author: D. Stanton
published in: European Journal of Combinatorics
publication date: 1999-03-08T00:00:00Z
review text: The determinant \(\text{det}\left(\delta_{ij}+ \left(\begin{smallmatrix} x+i+j\\ j\end{smallmatrix}\right)\right)\), \(0\leq i\), \(j\leq n-1\), arose in the enumeration of a certain set of plane partitions and was evaluated by \textit{W. H. Mills}, \textit{D. P. Robbins} and \textit{H. Rumsey} [Discrete Math. 67, 43-55 (1987; Zbl 0656.05006)]. The authors now give a new more concise proof of the result. Another proof can be obtained via the recent computer-aided approach of \textit{M. Petkovšek} and \textit{H. S. Wilf} [Electron. J. Comb. 3, No. 2, Paper R19, 3p. (1996; Zbl 0851.05005)].
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 1199949
zbMATH Keywords: determinant
zbMATH Keywords: enumeration
zbMATH Keywords: plane partitions
MaRDI profile type: Publication
full work available at URL: eujc.1997.0184
OpenAlex ID: W1990734676
DOI: 10.1006/EUJC.1997.0184
description: scientific article; zbMATH DE number 1199949