Abstract. In this paper, we explore the issue of minimizing the degrees on rational knots. We set a bound on these degrees using Bézout’s theorem, define minimal degree sequences for rational functions, and explore the degree sequences of the trefoil and figure-eight knots. This research was conducted at the Mount Holyoke College REU program during the summer of 2002. Special thanks go out to our advisors, Alan Durfee and Donal O’Shea, and the othe
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