Determinants of Normalized Bohemian Upper Hessemberg Matrices

Fasi, Massimiliano and Negri Porzio, Gian Maria (2019) Determinants of Normalized Bohemian Upper Hessemberg Matrices. [MIMS Preprint]

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Abstract

A matrix is Bohemian if its elements are taken from a finite set of integers. We enumerate all possible determinants of Bohemian upper Hessenberg matrices with subdiagonal fixed to one, and consider the special case of families of matrices with only zeros on the main diagonal, whose determinants proved to be related to a generalization of Fibonacci numbers. Several conjectures recently stated by Corless and Thornton follow from our results.

Item Type: MIMS Preprint
Uncontrolled Keywords: Bohemian matrix, upper Hessenberg matrix, determinant, Fibonacci number.
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
Depositing User: Mr Gian Maria Negri Porzio
Date Deposited: 15 May 2019 10:49
Last Modified: 15 May 2019 10:49
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2709

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