Date of Graduation
2016
Document Type
Thesis
Degree Type
MS
College
Eberly College of Arts and Sciences
Department
Mathematics
Committee Chair
Kevin G Milans
Committee Co-Chair
Harvey Diamond
Committee Member
Michael Mays
Abstract
The Chebyshev polynomials arise in several mathematical contexts such as approximation theory, numerical integration, and differential equations. Here we study a combinatorial interpretation of Chebyshev polynomials due to Shapiro, and we use it to give a slight variation of a combinatorial proof of Binet's Formula due to Benjamin, Derks and Quinn. Another beautiful formula for the Fibonacci numbers involves complex roots of unity. Presently, no combinatorial proof is known. We give combinatorial proofs of some related identities as progress toward a full combinatorial proof.
Recommended Citation
Wahyuni, Nurul, "Chebyshev Polynomials and Fibonacci Numbers" (2016). Graduate Theses, Dissertations, and Problem Reports. 6885.
https://researchrepository.wvu.edu/etd/6885