The generalized Fibonomial matrix

DOI10.1016/j.ejc.2009.03.041zbMath1184.15021OpenAlexW2024769264MaRDI QIDQ1041195

Emrah Kılıç

Publication date: 1 December 2009

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ejc.2009.03.041

zbMATH Keywords

generating functionscombinatorial identitieseigenvaluesdeterminantscharacteristic polynomialslinear recurrence relationPascal matrixgeneralized Fibonacci coefficientsgeneralized Fibonomial matrix

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Eigenvalues, singular values, and eigenvectors (15A18) Matrices of integers (15B36) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (7)

Fibonomial and Lucanomial sums through well-poised $q$-series ⋮ Formulæ for multi-parameter Gaussian \(q\)-binomial sums with applications ⋮ On the connectivity properties and energy of Fibonomial graphs ⋮ On Fibonomial sums identities with special sign functions: analytically q-calculus approach ⋮ A matrix approach for divisibility properties of the generalized Fibonacci sequence ⋮ A class of non-symmetric band determinants with the Gaussianq-binomial coefficients ⋮ Evaluation of Hessenberg determinants via generating function approach

Cites Work

• Netted matrices
• The combinatorial power of the companion matrix
• On some identities for the Fibonomial coefficients via generating function
• Generating functions for powers of a certain generalized sequence of numbers
• Sums of the squares of terms of sequence \(\{u_n\}\)
• Pascal Matrices
• Permanents of (0, 1)-Circulants
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