A Combinatorial Interpretation of the Padovan Generalized Polynomial Sequence

Renata Passos Machado Vieira; Francisco Regis Vieira Alves; Paula Maria Machado Cruz Catarino

doi:10.52737/18291163-2023.15.11-1-9

Authors

Renata Passos Machado Vieira Universidade Federal do Ceará https://orcid.org/0000-0002-1966-7097
Francisco Regis Vieira Alves Federal Institute of Science and Technology Education of the State of Ceará https://orcid.org/0000-0003-3710-1561
Paula Maria Machado Cruz Catarino University of Trás-os-Montes and Alto Douro https://orcid.org/0000-0001-6917-5093

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.

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