Disproving a conjecture of Thornton on Bohemian matrices
type: Item
instance of: scholarly article
title: Disproving a conjecture of Thornton on Bohemian matrices
zbMATH Open document ID: 1481.15038
author: Zhibin Du
author: Yingqiu Xu
author: Jiahao Ye
author: C. M.da Fonseca
published in: Open Mathematics
publication date: 2021-11-29T00:00:00Z
review text: The authors provide a counterexample for a conjecture about Hessenberg matrices. They establish several results which lead to the counterexample, thus concluding that the conjecture is false. For this counterexample, they use a matrix of order 10, but they claim that the conjecture is false for a matrix of order 11 as well. Some open problems are described in the last section. This paper is easy to read and it is an interesting source for future researchers.
reviewed by: Rosário Fernandes
Mathematics Subject Classification ID: 15B99
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 7435662
zbMATH Keywords: Bohemian matrix
zbMATH Keywords: integral matrix
zbMATH Keywords: normalized upper Hessenberg matrix
zbMATH Keywords: determinant
Wikidata QID: Q123186970
describes a project that uses: OEIS
MaRDI profile type: Publication
full work available at URL: math-2021-0045
OpenAlex ID: W3169964940
cites work: Some computational problems involving integral matrices
cites work: Matrices of rational integers
cites work: Upper Hessenberg and Toeplitz Bohemians
cites work: The bohemian eigenvalue project
cites work: Q3299345
cites work: Q4989740
cites work: Q4443440
cites work: An identity between the determinant and the permanent of Hessenberg-type matrices
cites work: Q3580572
cites work: Numerical algorithms for the determinant evaluation of general Hessenberg matrices
cites work: Evaluation of Hessenberg determinants via generating function approach
cites work: A note on the determinant of a Toeplitz-Hessenberg matrix
cites work: Some determinantal considerations for pentadiagonal matrices
cites work: A periodic determinantal property for (0,1) double banded matrices
DOI: 10.1515/MATH-2021-0045
description: scientific article; zbMATH DE number 7435662