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Minimal Degree Parameterizations of the Trefoil and Figure-Eight Knots

This paper determines the minimal degree sequence for two compact rational knots, namely the trefoil and figure-eight knots. We find explicit projections with the minimal degree sequence of each knot. This is done by modifying a non-compact rational minimal-degree parameterization of the trefoil and figure-eight knots to make it compact. This research was conducted at Ramapo College of New Jersey during the summer of 2011 with Dr. Donovan McFeron.

preprint2011arXivOpen access
Samantha Pezzimenti
math.GT
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Samantha Pezzimenti

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