We determine conditions under which an arbitrary polynomial can be expressed as the composition of two rational functions, generalizing the work of J. Rickards on the decomposition into two polynomials. We show that a polynomial can be expressed non-trivially as a composition of two rational functions if and only if it can be so decomposed into two polynomials.

Author Bio

Steven Carter graduated from Birmingham-Southern College in 2012 with a B.S. in mathematics and physics. The present work was conducted to fulfill the senior capstone research requirement in mathematics. Concurrently, he produced novel work on statistical gamma-ray transitions for the capstone research requirement in physics following his participation in a nuclear physics REU at Duke University in the summer of 2011. Carter received the Presidential Fellowship and is now a Ph.D. student at the Georgia Institute of Technology School of Physics at which he plans to study theoretical quantum mechanics.