Permanent of Toeplitz matrices with Narayana entries

Özen Özer, Selcuk Koyuncu, Wynn Kwiatkowski

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.


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References


T. Goy, On determinants and permanents of some Toeplitz-Hessenberg matrices whose entries are Jacobsthal numbers, Eurasian Math. J. 9 (2018), no. 4, 61-67.

T. Goy, On identities with multinomial coeffcients for Fibonacci-Narayana sequence, Ann. Math. Inform. 49 (2018), 75-84.

K. Kaygisiz, A. Sahin, Determinantal and permanental representations of Fibonacci type numbers and polynomials, Rocky Mountain J. Math. 46 (2016), no. 1, 227-242.

S. Koparal, N. Omur, C.D. Sener, Some permanents of Hessenberg matrices, Filomat 33 (2019), no. 2, 475-481.

G.Y. Lee, k-Lucas numbers and associated bipartite graphs, Linear Algebra Appl. 320 (2000), no. 1-3, 51-61.

J. Seibert, P. Trojovsky, On factorization of the Fibonacci and Lucas numbers using tridiagonal determinants, Math. Slovaca 62 (2012), no. 3, 439-450.




DOI: https://doi.org/10.52846/ami.v50i2.1716