A Combinatorial Interpretation of the Padovan Generalized Polynomial Sequence

Authors

DOI:

https://doi.org/10.52737/18291163-2023.15.11-1-9

Keywords:

Combinatorics, Generalization, Padovan Polynomial Sequence

Abstract

We investigate a combinatorial interpretation of the Padovan polynomial sequence, also addressing its polynomial extensions. We thus include the Tridovan polynomial sequence, Tetradovan polynomial sequences, leading up to the Z-dovan polynomial generalization.

Author Biographies

  • Renata Passos Machado Vieira, Universidade Federal do Ceará

    PhD student in Teaching at the Northeast Teaching Network (RENOEN-Polo UFC). Master in Teaching Science and Mathematics by the Federal Institute of Education, Science and Technology of the State of Ceará. Teacher at the Education Department of the State of Ceará.

  • Francisco Regis Vieira Alves, Federal Institute of Science and Technology Education of the State of Ceará

    Graduated in Bachelor of Mathematics from the Federal University of Ceará (1998), graduated in Mathematics from the Federal University of Ceará (1997), Master in Pure Mathematics from the Federal University of Ceará (2001) and Master in Education, with emphasis on Education Mathematics, Federal University of Ceará (2002). PhD with emphasis on Mathematics teaching (UFC - 2011).
    TITLE Professor at the Federal Institute of Education, Science and Technology of the state of Ceará / IFCE - 40h/a with DE, of the Degree in Mathematics and Research Productivity Scholarship from CNPq - Level (2020 - 2023). He has experience in the area of Mathematics and works mainly in the following subjects: Didactics of Mathematics, History of Mathematics, Real Analysis, Philosophy of Mathematics and Technologies applied to the teaching of Mathematics for higher education. With research focused on teaching Calculus I, II, III, Complex Analysis, ODE, Number Theory. And at the Open University of Brazil, with distance learning in Mathematics. Develops research aimed at teaching multi-variable calculus and its internal transition. He also works in the Professional Master's Degree in Teaching Science and Mathematics (ENCIMA) - UFC. Reviewer and ad hoc reviewer of the following journals: Vydya Educação, Sinergia - IFSP, Rencima - Magazine of Teaching Science and Mathematics, Magazine of the Geogebra Institute of São Paulo, Tear - Magazine of Education, Science and Technology, Online Bulletin of Mathematics Education - BoEM and REMAT magazine: Electronic Magazine of Mathematics. Editorial Committee of the Cearense Bulletin of Education and History of Mathematics (BOCEHM) and Coordinator of the Graduate Program in Science and Mathematics Teaching - PGECM/IFCE (academic). in the period 2015/2020 and Member of the Scientific Council of the journal ForSCience - IFMG. Evaluator of the EURASIA Journal of Mathematics, Science and Technology Education.

  • Paula Maria Machado Cruz Catarino, University of Trás-os-Montes and Alto Douro

    PhD in Mathematics. Associate Professor of UTAD (Universidade de Trás-os-Montes e Alto Douro) with habilitation. Researcher of Research Centre CMAT-UTAD- Polo of CMAT of University of Minho and also Researcher of the Research Centre CIDTFF - Research Centre “Didactics and Technology in Education of Trainers. Currently Member of General Council of UTAD.

References

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A.T. Benjamin and J.J. Quinn, The Fibonacci numbers-exposed more discretely. Math. Magazine, 76 (2003), no. 3, pp. 182-192. https://doi.org/10.1080/0025570x.2003.11953177

R.R. de Oliveira, Engenharia Didática sobre o Modelo de Complexificação da Sequência Generalizada de Fibonacci:Relações Recorrentes N-dimensionais e Representações Polinomiais e Matriciais. Dissertação (Mestrado) – Programa de Pós-Graduação em Ensino de Ciências e Matemática, Instituto Federal de Educação, Ciência e Tecnologia do Estado do Ceará, 2018.

T. Koshy, Fibonacci and Lucas numbers with applications, 2nd edition. New York: Wiley-Interscience, 2019.

E.V.P. Spreafico, Novas identidades envolvendo os números de Fibonacci, Lucas e Jacobsthal via ladrilhamentos, Doutorado em Matemática Aplicada, Universidade Estadual de Campinas - IME, 2014. https://doi.org/10.47749/t/unicamp.2014.937460

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R.P.M. Vieira, Engenharia Didática (ED): o caso da Generalizaçãoe Complexificação da Sequência de Padovan ou Cordonnier, Programa de Pós-Graduação em Ensino de Ciências e Matemática, Instituto Federal de Educação, Ciência e Tecnologia do Estado do Ceará, Mestrado em Ensino de Ciências e Matemática, 2020. https://doi.org/10.21713/rbpg.v16i2.1772

R.P.M. Vieira, F.R.V. Alves and P.M.M.C. Catarino, Combinatorial interpretation of numbers in the generalized Padovan sequence and some of its extensions. Axioms, 11 (2022), no. 11, pp. 1-9. https://doi.org/10.3390/axioms11110598

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Published

2023-11-28

Issue

Vol. 15 No. 11 (2023): A Combinatorial Interpretation of the Padovan Generalized Polynomial Sequence

Section

Articles

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Copyright (c) 2023 Armenian Journal of Mathematics

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

A Combinatorial Interpretation of the Padovan Generalized Polynomial Sequence. (2023). Armenian Journal of Mathematics, 15(11), 1-9. https://doi.org/10.52737/18291163-2023.15.11-1-9