Autour de la conjecture de Dyson. (Around the conjecture of Dyson)
type: Item
instance of: scholarly article
title: Autour de la conjecture de Dyson. (Around the conjecture of Dyson)
zbMATH Open document ID: 0685.05002
DOI: 10.1016/S0195-6698(89)80069-1
author: Laurent Habsieger
published in: European Journal of Combinatorics
publication date: 1989-01-01T00:00:00Z
review text: Given an n-tuple of positive integers, \((a_ 1,...,a_ n)\), let M be the set of words in \(a_ 1\) \(1's,...,a_ n\) n's and for \(w\in M\), let \(a_{ij}(w)\) be the number of i's to the left of the first j in w. Let \[ \phi_ w=\prod_{1\leq i\neq j\leq n}(1-\frac{x_ i}{x_ j})^{a_{ij}(w)},\quad \Phi =\prod_{1\leq i\neq j\leq n}(1-\frac{x_ i}{x_ j})^{a_ i}. \] The author proves that \(\Phi =\sum \phi_ w\), \(w\in M\), from which it is simple to derive Dyson's constant term conjecture [see \textit{I. G. Macdonald}, SIAM J. Math. Anal. 13, 988-1007 (1982; Zbl 0498.17006)]. The problems that arise in seeking a q-analog of this are discussed.
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 4121999
zbMATH Keywords: Dyson conjecture
Wikidata QID: Q122940229
reviewed by: David M. Bressoud
MaRDI profile type: Publication
cites work: Q4109912
cites work: Q4146776
cites work: Q5580319
cites work: Constant Term Identities Extending the q-Dyson Theorem
cites work: Statistical Theory of the Energy Levels of Complex Systems. I
cites work: Proof of a Conjecture by Dyson in the Statistical Theory of Energy Levels
cites work: Une q-Intégrale de Selberg et Askey
cites work: A Proof of Askey’s Conjectured q-Analogue of Selberg’s Integral and a Conjecture of Morris
cites work: Some Conjectures for Root Systems
cites work: A Short Proof of MacDonald's Conjecture for the Root Systems of Type A
cites work: Proof of a Conjecture by Dyson
cites work: A Stembridge-Stanton style elementary proof of the Habsieger-Kadell q- Morris identity
cites work: A proof of Andrews' \(q\)-Dyson conjecture
description: scientific article; zbMATH DE number 4121999