Carlos Fonseca – cmc.deusto.eus

A note on the eigenvalues of a Sylvester-Kac matrix with off-diagonal biperiodic perturbations

Z. Du, C.M. da Fonseca (2025) A note on the eigenvalues of a Sylvester-Kac matrix with off-diagonal biperiodic perturbations, Journal of Computational and Applied Mathematics 461 (2025) 116429, 10.1016/j.cam.2024.116429 Abstract.…

The determinant and a factorization of a Toeplitz matrix with some type of Horadam numbers entries,

C.M. da Fonseca, C. Kızılateş, N. (2024) The determinant and a factorization of a Toeplitz matrix with some type of Horadam numbers entries, Logic Journal of the IGPL, jzae065, 10.1093/jigpal/jzae065…

Revisiting some r-Fibonacci sequences and Hessenberg matrices

C.M. da Fonseca, P. Saraiva, A.G. Shannon (2024) Revisiting some -Fibonacci sequences and Hessenberg matrices, Notes on Number Theory and Discrete Mathematics, Vol. 30, pp. 704-715, 10.7546/nntdm.2024.30.4.704-715 Abstract. The relationship…

A new generalization of min and max matrices and their reciprocals counterparts

C.M. da Fonseca, C. Kızılateş, N. (2024) A new generalization of min and max matrices and their reciprocals counterparts, Filomat, Vol. 38, pp. 421-435, 10.2298/FIL2402421F Abstract. In this paper, we…

Equitable partitions and spectra of symmetric trees: Revisiting Heilbronner’s composition principle

M. Anđelić, C.M. da Fonseca (2024) Equitable partitions and spectra of symmetric trees: Revisiting Heilbronner's composition principle, Discrete Mathematics Letters, Vol. 14, pp. 108-117, 10.47443/dml.2024.160 Abstract. The notion of equitable…

On Chebyshev polynomials and the inertia of certain matrices

K. Castillo, C.M. da Fonseca, J. Petronilho (2024) On Chebyshev polynomials and the inertia of certain matrices, Applied Mathematics and Computation, Vol. 467, pp. 128-497, 10.1016/j.amc.2023.128497 Abstract. It was first…

A formal operator involving Fermatian numbers

C.M. da Fonseca, A.G. Shannon (2024) A formal operator involving Fermatian numbers, Notes on Number Theory and Discrete Mathematics, Vol. 30, pp. 491-498, 10.7546/nntdm.2024.30.3.491-498 Abstract. In this note, old and…

The generating function of a bi-periodic Leonardo sequence

C.M. da Fonseca (2024) The generating function of a bi-periodic Leonardo sequence, Armenian Journal of Mathematics, Vol. 16, pp. 1-8, 10.52737/18291163-2024.16.07-1-8 Abstract. In "A note on bi-periodic Leonardo sequence", the…

The determinants of certain double banded (0,1) Toeplitz matrices

Z. Du, C.M. da Fonseca (2023) The determinants of certain double banded (0,1) Toeplitz matrices, Miskolc Mathematical Notes, Vol. 24, pp.1307-1315, 10.18514/MMN.2023.4053 Abstract. We prove a conjecture proposed recently in…

On a sequence derived from the Laplace transform of the characteristic polynomial of the Fibonacci sequence

C.M. da Fonseca, A.G. Shannon (2023) On a sequence derived from the Laplace transform of the characteristic polynomial of the Fibonacci sequence, Notes on Number Theory and Discrete Mathematics, Vol.…

The number of P-vertices for acyclic matrices with given nullity

Z. Du, C.M. da Fonseca (2023) The number of P-vertices for acyclic matrices with given nullity, Discrete Mathematics, Vol. 346, pp.113-592, 10.1016/j.disc.2023.113592 Abstract. In this paper, we completely characterize those…

The characterization of the minimal weighted acyclic graphs

Z. Du, C.M. da Fonseca (2023) The characterization of the minimal weighted acyclic graphs, Linear Algebra and its Applications, Vol. 672, pp.75-92, 10.1016/j.laa.2023.04.019 Abstract. In this paper, we completely characterize…

Further developments of basic trigonometric power sums

Z. Du, C.M. da Fonseca, V. Kowalenko (2023) Further developments of basic trigonometric power sums, RACSAM Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas,…

Chain graph sequences and Laplacian spectra of chain graphs

A. Alazemi, M. Anđelić, K. Chandra, Carlos M. da Fonseca (2023) Chain graph sequences and Laplacian spectra of chain graphs, Linear and Multilinear Algebra, Vol. 74, pp.569-585, 10.1080/03081087.2022.2036672 Abstract. A…

Root location for the characteristic polynomial of a Fibonacci type sequence

Z. Du, C.M. da Fonseca (2023) Root location for the characteristic polynomial of a Fibonacci type sequence, Czechoslovak Mathematical Journal, Vol. 73, pp. 189-195, 10.21136/CMJ.2022.0043-22 Abstract. We analyse the roots…

A second-order difference equation with sign-alternating coefficients

M. Anđelić, C.M. da Fonseca, T. Koledin, Z. Stanić (2022) A second-order difference equation with sign-alternating coefficients, Kuwait Journal of Science, Vol. 50, No. 1, 10.48129/kjs.20425 Abstract. We provide an…

An extended eigenvalue-free interval for the eccentricity matrix of threshold graphs

M. Anđelić, C.M. da Fonseca, T. Koledin, Z. Stanić (2022) An extended eigenvalue-free interval for the eccentricity matrix of threshold graphs, Journal of Applied Mathematics and Computing 69 (2023) 491-503,…

A periodic determinantal property for (0,1) double banded matrices

Z. Du, C.M. da Fonseca (2022) A periodic determinantal property for (0,1) double banded matrices, Linear and Multilinear Algebra, Vol. 70, pp. 5316-5328, 10.1080/03081087.2021.1913980 Abstract. In this paper, we extend…

An identity involving derangement numbers and Bell numbers

Z. Du, C.M. da Fonseca (2022) An identity involving derangement numbers and Bell numbers, Applicable Analysis and Discrete Mathematics, Vol. 16, pp.485-494, 10.2298/AADM200705018D Abstract. The aim of this paper is…

On tridiagonal matrices associated with Jordan blocks

C.M. da Fonseca, V. Kowalenko (2022) On tridiagonal matrices associated with Jordan blocks, Acta Universitatis Sapientiae, Mathematica, Vol. 14, pp.61-74, 10.2478/ausm-2022-0004 Abstract. This paper aims to show how some standard…

A Sylvester-Kac matrix type and the Laplacian controllability of half graphs

M. Anđelić, C.M. da Fonseca, E. Kılıç, Z. Stanic (2022) New strong divisibility sequences, Electronic Journal of Linear Algebra, Vol. 38, pp. 559-571, 10.13001/ela.2022.6947 Abstract. In this paper, we provide…

New strong divisibility sequences

Z. Du, C.M. da Fonseca, D. Dimitrov (2022) New strong divisibility sequences, Ars Mathematica Contemporanea, Vol. 22, P1.08, 10.26493/1855-3974.2473.f2e Abstract. We provide new families of divisibility and strong divisibility sequences…

The bi-periodic Horadam sequence and some perturbed tridiagonal 2-Toeplitz matrices: A unified approach

Milica Anđelić, C.M. da Fonseca, Fatih Yılmaz (2022) Determinantal representations for the number of subsequences without isolated odd terms, Heliyon, Vol. 8, E08863, 10.1016/j.heliyon.2022.e08863 Abstract. In this note we consider…

Determinantal representations for the number of subsequences without isolated odd terms

Milica Anđelić, C.M. da Fonseca (2021) Determinantal representations for the number of subsequences without isolated odd terms, Notes on Number Theory and Discrete Mathematics 27 (2021) 116-121, 10.7546/nntdm.2021.27.4.116-121 Abstract. In…

On the constant coefficients of a certain recurrence relation: A simple proof

Milica Anđelić, C.M. da Fonseca (2021) On the constant coefficients of a certain recurrence relation: A simple proof, Heliyon, Vol. 7, E07764, 10.1016/j.heliyon.2021.e07764 Abstract. In this note, we provide a…

The spectrum of a new class of Sylvester-Kac matrices

A. Alazemi, C.M. da Fonseca, E. Kılıç (2021) The spectrum of a new class of Sylvester-Kac matrices, Filomat, Vol. 35, pp.4017-4031, 10.2298/FIL2112017A Abstract. We define a new class of Sylvester-Kac…

Disproving a conjecture of Thornton on Bohemian matrices

Z. Du, C.M. da Fonseca, Y. Xu, J. Ye (2021) Disproving a conjecture of Thornton on Bohemian matrices, Open Mathematics, Vol. 19, pp. 505-514, 10.1515/math-2021-0045 Abstract. In this paper, we…

Three representation types for systems of forms and linear maps

A. Alazemi, M. Anđelić, C.M. da Fonseca, V. Futorny, V.V. Sergeichuk (2021) Three representation types for systems of forms and linear maps, Mathematics, Vol. 9, No. 455, 10.3390/math9050455 Abstract. We…