Carlos M. da Fonseca

Carlos M. da Fonseca

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My main field of research is combinatorial matrix theory and spectral graph theory, and their abundant multi-disciplinary applications. I am also interested in trigonometric sums and the connections between abstract and linear algebras.

External Scientific Member
Kuwait College of Science and Technology
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Carlos Martins da Fonseca (Figueira da Foz, Portugal, 1968) is a full professor at the Kuwait College of Science and Technology. He is Doctor of Science by the Technical University – Sofia, Bulgaria. He is the editor-in-chief of Special Matrices, a journal on structured matrices by De Gruyter.

• DSc. in Mathematics (2016), Technical University – Sofia, Bulgaria
• PhD in Mathematics (1996 – 2000), University of Coimbra, Portugal
• BSc. in Mathematics (1986 – 1991), University of Coimbra, Portugal

  

 

Research interests

My main field of research is combinatorial matrix theory and spectral graph theory, and their abundant multi-disciplinary applications.
I am also interested in trigonometric sums and the connections between abstract and linear algebras.

 

 

Publications

2026

• An\djeli\’c, M., da Fonseca, C. M., & Stani\’c, Z. (2026). An equitable partition based construction of graphs with the same spectral radius. Appl. Math. Comput., 510, 6. https://doi.org/10.1016/j.amc.2025.129696
• da Fonseca, C. M. (2026). A comment on the spectrum of a four-parameter extension of the Sylvester-Kac matrix. J. Comput. Appl. Math., 472, 3. https://doi.org/10.1016/j.cam.2025.116786

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2025

• da Fonseca, C. M. (2025). On the generating functions of products mixing two \(k\)-Fibonacci and other sequences. Georgian Math. J., 32(6), 933–938. https://doi.org/10.1515/gmj-2025-2030
• da Fonseca, C. M., K\iz\ilate\cs, C., & Terzio\uglu, N. (2025). The determinant and a factorization of a Toeplitz matrix with some type of Horadam numbers entries. Log. J. IGPL, 33(6), 13. https://doi.org/10.1093/jigpal/jzae065
• da Fonseca, C. M., K\iz\ilate\cs, C., Saraiva, P., & Shannon, A. G. (2025). Generalised Leonardo numbers. Log. J. IGPL, 33(6), 12. https://doi.org/10.1093/jigpal/jzaf005
• da Fonseca, C. M., Kizilate\cs, C., & Terzio\uglu, N. (2025). The determinants and the inverses of the \(\left(\frac2ak^2+2,a,a\right)\)-\(L_k\)-Toeplitz and the \((2,k^2+2,k^2+2)\)-\(F_k\)-Toeplitz matrices. Log. J. IGPL, 33(6), 17. https://doi.org/10.1093/jigpal/jzaf003
• da Fonseca, C. M., Glasser, M. L., & Kowalenko, V. (2025). New identities involving the univariate Lommel and Bessel functions. Appl. Anal. Discrete Math., 19(2), 348–369. https://doi.org/10.2298/AADM240809015F
• Du, Z. & da Fonseca, C. M. (2025). General Sylvester-Kac matrices with plain eigenvalues. Comput. Appl. Math., 44(8), 19. https://doi.org/10.1007/s40314-025-03352-2
• da Fonseca, C. M., Glasser, M. L., & Kowalenko, V. (2025). Chebyshev polynomials of the first kind and the univariate Lommel function: integral representations. Open Math., 23, 16. https://doi.org/10.1515/math-2024-0113
• Du, Z. & da Fonseca, C. M. (2025). New families of trees determined by their spectra. Linear Algebra Appl., 722, 101–113. https://doi.org/10.1016/j.laa.2025.05.007
• Du, Z. & da Fonseca, C. M. (2025). The real symmetric matrices with a given rank and a \(\mathrmP\)-set with maximum size. Discrete Math., 348(11), 8. https://doi.org/10.1016/j.disc.2025.114572
• Du, Z. & da Fonseca, C. M. (2025). A note on the eigenvalues of a Sylvester-Kac type matrix with off-diagonal biperiodic perturbations. J. Comput. Appl. Math., 461, 6. https://doi.org/10.1016/j.cam.2024.116429

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2024

• An\djeli\’c, M. & da Fonseca, C. M. (2024). Equitable partitions and spectra of symmetric trees: revisiting Heilbronner's composition principle. DML, Discrete Math. Lett., 14, 108–117. https://doi.org/10.47443/dml.2024.160
• Du, Z. & da Fonseca, C. M. (2024). Sylvester-Kac matrices with quadratic spectra: a comprehensive note. Ramanujan J., 65(3), 1313–1322. https://doi.org/10.1007/s11139-024-00940-4
• da Fonseca, C. M. (2024). The generating function of a bi-periodic Leonardo sequence. Armen. J. Math., 16, 8. https://doi.org/10.52737/18291163-2024.16.07-1-8
• Du, Z. & da Fonseca, C. M. (2024). Correction and some comments to: “A periodic determinantal property for \((0,1)\) double banded matrices''. Linear Multilinear Algebra, 72(8), 1254–1258. https://doi.org/10.1080/03081087.2023.2176415
• Castillo, K., da Fonseca, C. M., & Petronilho, J. (2024). On Chebyshev polynomials and the inertia of certain tridiagonal matrices. Appl. Math. Comput., 467, 8. https://doi.org/10.1016/j.amc.2023.128497
• Dyachenko, A., da Fonseca, C. M., & Tyaglov, M. (2024). $a$-potent Schwarz matrices and Bessel-like Jacobi polynomials. (Unpublished, Submitted). arXiv: 2406.11032
• An\djeli\’c, M., da Fonseca, C. M., Futorny, V., & Tsylke, A. (2024). Gelfand-Tsetlin modules for Lie algebras of rank $2$. (Unpublished, Submitted). arXiv: 2402.00483

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2023

• An\djeli\’c, M. & Da Fonseca, C. M. (2023). On a determinantal formula for derangement numbers. Kragujevac J. Math., 47(6), 847–850.
• Du, Z. & da Fonseca, C. M. (2023). The determinants of certain double banded \((0,1)\) Toeplitz matrices. Miskolc Math. Notes, 24(3), 1307–1315. https://doi.org/10.18514/MMN.2023.4053
• Du, Z. & da Fonseca, C. M. (2023). The number of P-vertices for acyclic matrices with given nullity. Discrete Math., 346(12), 17. https://doi.org/10.1016/j.disc.2023.113592
• Du, Z. & da Fonseca, C. M. (2023). The characterization of the minimal weighted acyclic graphs. Linear Algebra Appl., 672, 75–92. https://doi.org/10.1016/j.laa.2023.04.019
• Du, Z., da Fonseca, C. M., & Kowalenko, V. (2023). Further developments of basic trigonometric power sums. Rev. R. Acad. Cienc. Exactas F\’\is. Nat., Ser. A Mat., RACSAM, 117(3), 17. https://doi.org/10.1007/s13398-023-01442-6
• Alazemi, A., An\djeli\’c, M., Das, K. C., & da Fonseca, C. M. (2023). Chain graph sequences and Laplacian spectra of chain graphs. Linear Multilinear Algebra, 71(4), 569–585. https://doi.org/10.1080/03081087.2022.2036672
• An\djeli\’c, M., da Fonseca, C. M., Koledin, T., & Stani\’c, Z. (2023). An extended eigenvalue-free interval for the eccentricity matrix of threshold graphs. J. Appl. Math. Comput., 69(1), 491–503. https://doi.org/10.1007/s12190-022-01758-3
• da Fonseca, C. M., K\iz\ilate\cs, C., & Terzio\uglu, N. (2023). A second-order difference equation with sign-alternating coefficients. Kuwait J. Sci., 50(2A), 8. https://doi.org/10.48129/kjs.20425
• Du, Z. & da Fonseca, C. M. (2023). Root location for the characteristic polynomial of a Fibonacci type sequence.. Czech. Math. J., 73(1), 189–195. https://doi.org/10.21136/CMJ.2022.0043-22

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2022

• Du, Z. & da Fonseca, C. M. (2022). A periodic determinantal property for \((0,1)\) double banded matrices. Linear Multilinear Algebra, 70(20), 5316–5328. https://doi.org/10.1080/03081087.2021.1913980
• da Fonseca, C. M. & Kowalenko, V. (2022). On tridiagonal matrices associated with Jordan blocks. Acta Univ. Sapientiae, Math., 14(1), 61–74. https://doi.org/10.2478/ausm-2022-0004
• Du, Z. & da Fonseca, C. M. (2022). An identity involving derangement numbers and Bell numbers. Appl. Anal. Discrete Math., 16(2), 485–494. https://doi.org/10.2298/AADM200705010D
• Andelic, M., Da Fonseca, C. M., Kilic, E., & Stanic, Z. (2022). A Sylvester-Kac matrix type and the Laplacian controllability of half graphs. Electron. J. Linear Algebra, 38, 559–571.
• Du, Z., da Fonseca, C. M., & Pereira, A. (2022). On determinantal recurrence relations of banded matrices. Kuwait J. Sci., 49(1), 9. https://doi.org/10.48129/kjs.v49i1.11165
• Du, Z., Dimitrov, D., & da Fonseca, C. M. (2022). New strong divisibility sequences. Ars Math. Contemp., 22(1), 13. https://doi.org/10.26493/1855-3974.2473.f2e

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2021

• da Fonseca, C. M. (2021). Some comments on the properties of a particular tridiagonal matrix. J. Discrete Math. Sci. Cryptography, 24(1), 49–51. https://doi.org/10.1080/09720529.2019.1669920
• da Fonseca, C. M. (2021). On some quasi anti-tridiagonal matrices. J. Discrete Math. Sci. Cryptography, 24(4), 1043–1052. https://doi.org/10.1080/09720529.2020.1859800
• Du, Z., da Fonseca, C. M., Xu, Y., & Ye, J. (2021). Disproving a conjecture of Thornton on Bohemian matrices. Open Math., 19, 505–514. https://doi.org/10.1515/math-2021-0045
• An\djeli\’c, M. & da Fonseca, C. M. (2021). Some determinantal considerations for pentadiagonal matrices. Linear Multilinear Algebra, 69(16), 3121–3129. https://doi.org/10.1080/03081087.2019.1708845
• da Fonseca, C. M. & K\il\iç, E. (2021). A new type of Sylvester-Kac matrix and its spectrum. Linear Multilinear Algebra, 69(6), 1072–1082. https://doi.org/10.1080/03081087.2019.1620673

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