• Corpus ID: 251741208

The Fibonacci decomposition of symmetric Tetranacci polynomials

@inproceedings{Leumer2022TheFD,
  title={The Fibonacci decomposition of symmetric Tetranacci polynomials},
  author={Nico Leumer},
  year={2022}
}
. In this manuscript, we introduce (symmetric) Tetranacci polynomials ξ j as a twofold generalization of ordinary Tetranacci numbers, by considering both non unity coefficients and generic initial values in their recursive definition. The issue of these polynomials arose in condensed matter physics and the diagonalization of symmetric Toeplitz matrices having in total four non-zero off diagonals. For the latter, the symmetric Tetranacci polynomials are the basic entities of the associated… 

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A closed form expression is given for the eigenvalues and eigenvectors of a symmetric tridiagonal matrix of odd order whose diagonal elements are all equal and whoes superdiagonal elements alternate