Tribonacci properties of identities, matrices, and determinants
Number Theory
2026-05-26 v1 Combinatorics
Abstract
This paper considers the properties of Tribonacci numbers on identities, matrices, and determinants. In the first front part, we obtain several symmetric identities of Tribonacci numbers by a matrix-based approach and binomial inversion technique. In the core section of the latter half, we present a determinant representation of Tribonacci numbers in a slightly modified Toeplitz--Hessenberg form derived from Bell polynomials.
Keywords
Cite
@article{arxiv.2605.24853,
title = {Tribonacci properties of identities, matrices, and determinants},
author = {Takao Komatsu and Tengfei Shen},
journal= {arXiv preprint arXiv:2605.24853},
year = {2026}
}
Comments
Part of this paper is an excerpt from the master's thesis of the second-named author