Combinatorial proofs of Fibonacci identities

Harold R.L. Yang

doi:10.1117/12.2639169

19 May 2022 Combinatorial proofs of Fibonacci identities

Harold R.L. Yang

Proceedings Volume 12259, 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022); 122591F (2022) https://doi.org/10.1117/12.2639169
Event: 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022), 2022, Kunming, China

Abstract

In the book “Proofs that Really Count”, A. T. Benjamin and J. J. Quinn provided several identities involving Fibonacci numbers and left some unproved ones. Krzywkowski found that coverings in an area with dimension 2n can be enumerated by Fibonacci numbers. In this paper, by applying the combinatorial interpretation provided by Krzywkowski, we give combinatorial proofs of three unproved identities in the book “Proofs that Really Count”

Citation Download Citation

Harold R.L. Yang "Combinatorial proofs of Fibonacci identities", Proc. SPIE 12259, 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022), 122591F (19 May 2022); https://doi.org/10.1117/12.2639169

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