scholarly journals Determinants of Normalized Bohemian Upper Hessenberg Matrices

2020 ◽  
Vol 36 (36) ◽  
pp. 352-366
Author(s):  
Massimiliano Fasi ◽  
Gian Maria Negri Porzio
Keyword(s):  
Fibonacci Numbers ◽  
Main Diagonal ◽  
Hessenberg Matrix ◽  
Hessenberg Matrices ◽  
Finite Set

A matrix is Bohemian if its elements are taken from a finite set of integers. An upper Hessenberg matrix is normalized if all its subdiagonal elements are ones, and hollow if it has only zeros along the main diagonal. All possible determinants of families of normalized and hollow normalized Bohemian upper Hessenberg matrices are enumerated. It is shown that in the case of hollow matrices the maximal determinants are related to a generalization of Fibonacci numbers. Several conjectures recently stated by Corless and Thornton follow from these results.

scholarly journals Some Properties of Convolved k-Fibonacci Numbers

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
José L. Ramírez
Keyword(s):  
Fibonacci Numbers ◽  
Lucas Numbers ◽  
Hessenberg Matrices ◽  
Combinatorial Formulas

We define the convolved k-Fibonacci numbers as an extension of the classical convolved Fibonacci numbers. Then we give some combinatorial formulas involving the k-Fibonacci and k-Lucas numbers. Moreover we obtain the convolved k-Fibonacci numbers from a family of Hessenberg matrices.

scholarly journals A note on Pell-Padovan numbers and their connection with Fibonacci numbers

2020 ◽  
Vol 12 (2) ◽  
pp. 280-288
Author(s):  
T.P. Goy ◽  
S.V. Sharyn
Keyword(s):  
Fibonacci Numbers ◽  
Hessenberg Matrices ◽  
Sums Of Products ◽  
Fibonacci Sequences ◽  
Multinomial Coefficients ◽  
Connection Formulas

In this paper, we find new relations involving the Pell-Padovan sequence which arise as determinants of certain families of Toeplitz-Hessenberg matrices. These determinant formulas may be rewritten as identities involving sums of products of Pell-Padovan numbers and multinomial coefficients. In particular, we establish four connection formulas between the Pell-Padovan and the Fibonacci sequences via Toeplitz-Hessenberg determinants.

scholarly journals Inverse Eigenvalue Problem of Unitary Hessenberg Matrices

2009 ◽  
Vol 2009 ◽  
pp. 1-11
Author(s):  
Chunhong Wu ◽  
Linzhang Lu
Keyword(s):  
Eigenvalue Problem ◽  
Numerical Algorithm ◽  
Inverse Eigenvalue Problem ◽  
Theoretic Analysis ◽  
Hessenberg Matrix ◽  
Hessenberg Matrices ◽  
Principal Submatrix ◽  
Inverse Eigenvalue ◽  
Maximal Eigenvalues

LetH∈ℂn×nbe ann×nunitary upper Hessenberg matrix whose subdiagonal elements are all positive, letHkbe thekthleading principal submatrix ofH, and letH˜kbe a modified submatrix ofHk. It is shown that when the minimal and maximal eigenvalues ofH˜k(k=1,2,…,n) are known,Hcan be constructed uniquely and efficiently. Theoretic analysis, numerical algorithm, and a small example are given.

scholarly journals On prime factors of the sum of two k-Fibonacci numbers

2018 ◽  
Vol 14 (04) ◽  
pp. 1171-1195
Author(s):  
Carlos Alexis Gómez Ruiz ◽  
Florian Luca
Keyword(s):  
Lower Bound ◽  
Prime Factor ◽  
Fibonacci Numbers ◽  
Prime Factors ◽  
Finite Set ◽  
Generalized Fibonacci Sequences ◽  
Fibonacci Sequences ◽  
Positive Integers

We consider for integers [Formula: see text] the [Formula: see text]-generalized Fibonacci sequences [Formula: see text], whose first [Formula: see text] terms are [Formula: see text] and each term afterwards is the sum of the preceding [Formula: see text] terms. We give a lower bound for the largest prime factor of the sum of two terms in [Formula: see text]. As a consequence of our main result, for every fixed finite set of primes [Formula: see text], there are only finitely many positive integers [Formula: see text] and [Formula: see text]-integers which are a non-trivial sum of two [Formula: see text]-Fibonacci numbers, and all these are effectively computable.

scholarly journals Hessenberg matrices and the generalized Fibonacci-Narayana sequence

Filomat ◽  
2015 ◽  
Vol 29 (7) ◽  
pp. 1557-1563
Author(s):  
José Ramírez
Keyword(s):  
Hessenberg Matrix ◽  
Hessenberg Matrices

In this note, we define the generalized Fibonacci-Narayana sequence {Gn(a,b,c)}n?N. After that, we derive some relations between these sequences, and permanents and determinants of one type of upper Hessenberg matrix.

Non-repetitive sequences

1970 ◽  
Vol 68 (2) ◽  
pp. 267-274 ◽  
Author(s):  
P. A. B. Pleasants
Keyword(s):  
Repetitive Sequences ◽  
Finite Set ◽  
Infinite Sequences

This note is concerned with infinite sequences whose terms are chosen from a finite set of symbols. A segment of such a sequence is a set of one or more consecutive terms, and a repetition is a pair of finite segments that are adjacent and identical. A non-repetitive sequence is one that contains no repetitions.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

scholarly journals A Novel Simplified Implementation of Finite-Set Model Predictive Control for Power Converters

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Jose J. Silva ◽  
Jose R. Espinoza ◽  
Jaime A. Rohten ◽  
Esteban S. Pulido ◽  
Felipe A. Villarroel ◽  
...  
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Power Converters ◽  
Finite Set
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