A generalized Vandermonde determinant
type: Item
instance of: scholarly article
title: A generalized Vandermonde determinant
zbMATH Open document ID: 0773.05008
DOI: 10.1023/A:1022468019197
author: Marshall W. Buck
author: Raymond Coley
author: David P. Robbins
published in: Journal of Algebraic Combinatorics
publication date: 1993-03-15T00:00:00Z
review text: The Vandermonde determinant identity is given by \[ \text{det}(x^ j_ i)_{i,j=0,\dots,m}=\prod_{0\leq i<j\leq m}(x_ j-x_ i). \] In this paper two determinantal identities that generalize the Vandermonde determinant identity are established. In the first of the identities the set \(\{0,\dots,m\}\) indexing the rows and columns of the determinant is replaced by an arbitrary finite order ideal in the set of sequences of nonnegative integers which are 0 except for a finite number of terms. In the second the index set is replaced by an arbitrary finite order ideal in the set of all partitions.
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 05A18
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 130435
zbMATH Keywords: Vandermonde determinant
zbMATH Keywords: order ideal
zbMATH Keywords: partitions
reviewed by: Ratnakaram Nava Mohan
MaRDI profile type: Publication
cites work: Enumeration of subspaces by dimension sequence
full work available at URL: a:1022468019197
OpenAlex ID: W1564956404
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description: scientific article; zbMATH DE number 130435