Recursive and Combinational Formulas for Permanents of General k-tridiagonal Toeplitz Matrices

Abstract

This study on the permanents of the k−tridiagonal Toeplitz matrices includes recursive relations obtained by the reduction of the matrices to the other matrices whose permanents are easily calculable. These recursive relations are composed by writing the permanents with bandwidth k in terms of the permanents with bandwith smaller than k. Based on these recursive relations, an algorithm is given to calculate the permanents of k − tridiagonal Toeplitz matrices. Furthermore, explicit combinational formulas which are obtained using some of these recurrences, for the permanents are also presented here.