English

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