Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 52 min ago
PreprintarXiv licencearXiv

Inverse powers and 2-adic properties of binary 3 x 3 matrices associated with the Tribonacci sequence

  • Wilson Arley Martinez
  • Samin Ingrith Ceron
Open at sourcePDFDOICite

Abstract

In this paper, we study binary 3 x 3 matrices with determinant one that generate the Tribonacci recurrence. Starting from a specific generating matrix, we obtain explicit expressions for its powers and inverse powers in terms of the Tribonacci sequence T_n and two associated sequences B_n and R_n. This matrix framework yields identities involving traces, determinants, and products, including addition formulas and Cassini-type relations linking T_n, B_n, and Rn. Moreover, we derive new identities from the matrix representation of inverse powers and establish structural relations between these sequences. As an application, we investigate arithmetic properties of Tribonacci numbers and determine the exact 2-adic valuation of T_2^k for sufficiently large k. Finally, we provide a classification of 3 x 3 matrices associated with the Tribonacci recurrence via similarity over Q.

Related

  1. On periods of the Tribonacci sequence modulo primes
    Liam Baker, Florian Luca, Kerry Porrill
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. The generalized core-EP inverse of operator matrices with generalized Schur complements
    Huanyin Chen
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. A Note on the Drazin Inverse of 2 × 2 Block Triangular Matrices
    Ziyang Pan, Zhiping Xiong, Yingying Qin
    AxiomsPeer-reviewedCC BY 4.0General mathematicsCrossref
  4. Graphs of Moore-Penrose inverse of matrices possessing the treeangle property
    A. M. Encinas, K. Kranthi Priya, K. C. Sivakumar
    arXivPreprintCC0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  5. A higher order family of iterative methods for approximating inverse and generalized inverse matrices
    Alicia Cordero, Bushra Rani, Juan R. Torregrosa
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingarXiv

Cite

BibTeXRIS
BibTeX
@misc{martinez2026inverse,
  title = {{Inverse powers and 2-adic properties of binary 3 x 3 matrices associated with the Tribonacci sequence}},
  author = {Wilson Arley Martinez and Samin Ingrith Ceron},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04855},
  eprint = {2611.04855},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04855},
}
RIS
TY  - UNPB
TI  - Inverse powers and 2-adic properties of binary 3 x 3 matrices associated with the Tribonacci sequence
AU  - Wilson Arley Martinez
AU  - Samin Ingrith Ceron
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04855
UR  - https://arxiv.org/abs/2611.04855
AB  - In this paper, we study binary 3 x 3 matrices with determinant one that generate the Tribonacci recurrence. Starting from a specific generating matrix, we obtain explicit expressions for its powers and inverse powers in terms of the Tribonacci sequence T_n and two associated sequences B_n and R_n. This matrix framework yields identities involving traces, determinants, and products, including addition formulas and Cassini-type relations linking T_n, B_n, and Rn. Moreover, we derive new identities from the matrix representation of inverse powers and establish structural relations between these sequences. As an application, we investigate arithmetic properties of Tribonacci numbers and determine the exact 2-adic valuation of T_2^k for sufficiently large k. Finally, we provide a classification of 3 x 3 matrices associated with the Tribonacci recurrence via similarity over Q.
ER  -