ANALYSIS OF A NON-LINEAR RECURRENCE FORMULATED USING MATRIX PERMANENTS

In this study, we focus on reanalyzing and reducing a recursive formula that generates the permanents of a family of matrices called k-tridiagonal Toeplitz. This recursive formula is dependent on two free variables and is in non-linear form. We first propose an alternative proof to the one given in “Recursive and combinational formulas for permanents of general k-tridiagonal Toeplitz matrices”. This alternative proof is derived from a detailed examination of the designs of the submatrix blocks resulting from the expansion of permanents. Subsequently, we reduce this recursive formula to a linear form. This linear recursive formula simplifies the computation process by effectively reducing k-tridiagonal Toeplitz matrix permanents to those with a bandwidth of 1.