Permanent of Toeplitz matrices with Narayana entries

Abstract

In this paper, we investigate the properties of Toeplitz matrices with entries derived from the Narayana sequence. We demonstrate that when constructing Toeplitz matrices using Narayana numbers in a specific manner, their permanents exhibit a unique relationship, characterized as an exponential function. This novel finding offers new insights into the interplay between Toeplitz matrices and the Narayana sequence, expanding our understanding of the mathematical properties and potential applications of both.