Date of Award
5-2025
Document Type
Thesis
Degree Name
Bachelor of Science
Department
Math & Statistics
First Advisor
Dr. William Ross
Second Advisor
Dr. Ovidiu Lipan
Abstract
We explore polynomial composition through Ritt’s Theorem and mondromy groups. J.F. Ritt asked the question of when a polynomial can be written as the composition of two other polynomials of smaller, nontrivial degree. Ritt’s Theorem provides a method for determining whether or not a polynomial is composite by observing the actions of its associated monodromy group, a group of permutations acting upon the roots of a given polynomial. In this work, we study the monodromy groups of the Chebyshev polynomials of the first and second kinds to uncover their compositional properties.
Recommended Citation
Neuhaus, Eric, "Ritt’s Theorem and the Chebyshev Polynomials" (2025). Honors Theses. 1844.
https://scholarship.richmond.edu/honors-theses/1844
