A proof of the \(n!\) conjecture for generalized hooks
type: Item
instance of: scholarly article
title: A proof of the \(n!\) conjecture for generalized hooks
zbMATH Open document ID: 0854.05100
author: Ethan Reiner
published in: Journal of Combinatorial Theory. Series A
publication date: 1996-07-24T00:00:00Z
review text: \textit{A. M. Garsia} and \textit{M. Haiman} [Electron. J. Comb. 3, No. 2, Paper R24, 60 p. (1996)] posed the following conjecture about Macdonald polynomials \(H_\mu(x; q, t)\): for a partition \(\mu\) of \(n\), a determinant polynomial \(\Delta_\mu(X_n, Y_n)\) has \(n!\) linearly independent partial derivatives, i.e. the dimension of the vector space of these derivatives is \(n!\). The author proves this conjecture, using some previous results of the above-mentioned authors and himself.
reviewed by: Indulis Strazdins
Mathematics Subject Classification ID: 05E05
zbMATH DE Number: 909610
zbMATH Keywords: \(n\)! conjecture
zbMATH Keywords: generalized hooks
zbMATH Keywords: Ferrers diagram
zbMATH Keywords: Schur function
zbMATH Keywords: Macdonald polynomials
zbMATH Keywords: partial derivatives
Wikidata QID: Q122947702
MaRDI profile type: Publication
full work available at URL: jcta.1996.0060
OpenAlex ID: W2090826490
DOI: 10.1006/JCTA.1996.0060
description: scientific article; zbMATH DE number 909610