Reduction formulas for permanents and determinants of k-tridiagonal Toeplitz matrices

This study presents some results on the permanents of k-tridiagonal matrices with the Toeplitz structure. Our investigation establishes significant connections between the permanents of this matrix family and their reduced forms in terms of bandwidth and order. We extend the investigation also to the determinants of this matrix family in this context. Moreover, we demonstrate that some subforms of k-tridiagonal Toeplitz permanents can be effectively computed using the Pascal and Lucas triangles. Finally, we make a significant contribution by revealing an integer sequence related to Fibonacci numbers, derived by analyzing the permanents of some subforms of k-tridiagonal Toeplitz matrices.