Perrin’s bivariate and complex polynomials

Renata Passos Machado Vieira, Milena Carolina dos Santos Mangueira, Francisco Regis Vieira Alves and Paula Maria Machado Cruz Catarino
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 2, Pages 70—78
DOI: 10.7546/nntdm.2021.27.2.70-78
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Authors and affiliations

Renata Passos Machado Vieira
Department of Mathematics
Federal Institute of Education, Science, Technology of Ceara – IFCE ´
Treze of Maio, Brazil

Milena Carolina dos Santos Mangueira
Department of Mathematics
Federal Institute of Education, Science, Technology of Ceara – IFCE ´
Treze of Maio, Brazil

Francisco Regis Vieira Alves
Department of Mathematics
Federal Institute of Education, Science, Technology of Ceara – IFCE ´
Treze of Maio, Brazil

Paula Maria Machado Cruz Catarino
Department of Mathematics, University of Trás-os-Montes and Alto Douro
Portugal

Abstract

In this article, a study is carried out around the Perrin sequence, these numbers marked by their applicability and similarity with Padovan’s numbers. With that, we will present the recurrence for Perrin’s polynomials and also the definition of Perrin’s complex bivariate polynomials. From this, the recurrence of these numbers, their generating function, generating matrix and Binet formula are defined.

Keywords

  • Perrin complex bivariate polynomials
  • Perrin polynomials
  • Perrin sequence

2020 Mathematics Subject Classification

  • 11B37
  • 11B39

References

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Cite this paper

Vieira, R. P. M., Mangueira, M. C. S., Alves F. R. A., & Catarino, P. M. M. C. (2021). Perrin’s bivariate and complex polynomials. Notes on Number Theory and Discrete Mathematics, 27(2), 70-78, doi: 10.7546/nntdm.2021.27.2.70-78.

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