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Distance Fibonacci Polynomials by Graph Methods
- Source :
- Symmetry, Volume 13, Issue 11, Symmetry, Vol 13, Iss 2075, p 2075 (2021)
- Publication Year :
- 2021
- Publisher :
- Multidisciplinary Digital Publishing Institute, 2021.
-
Abstract
- In this paper we introduce and study a new generalization of Fibonacci polynomials which generalize Fibonacci, Jacobsthal and Narayana numbers, simultaneously. We give a graph interpretation of these polynomials and we obtain a binomial formula for them. Moreover by modification of Pascal’s triangle, which has a symmetric structure, we obtain matrices generated by coefficients of generalized Fibonacci polynomials. As a consequence, the direct formula for generalized Fibonacci polynomials was given. In addition, we determine matrix generators for generalized Fibonacci polynomials, using the symmetric matrix of initial conditions.
- Subjects :
- Fibonacci number
Mathematics::Combinatorics
Physics and Astronomy (miscellaneous)
General Mathematics
Mathematics::History and Overview
Fibonacci numbers
Pascal's triangle
Binomial theorem
Pascal’s triangle
Narayana number
Combinatorics
Matrix (mathematics)
symbols.namesake
Chemistry (miscellaneous)
Fibonacci polynomials
QA1-939
Computer Science (miscellaneous)
symbols
Graph (abstract data type)
Symmetric matrix
matrix generators
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Database :
- OpenAIRE
- Journal :
- Symmetry
- Accession number :
- edsair.doi.dedup.....ccab85ac00d13c116e3437de5c3808d7
- Full Text :
- https://doi.org/10.3390/sym13112075