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math.GT2025
Constructions of and Bounds on the Toric Mosaic Number
Kendall Heiney, Margaret Kipe, Samantha Pezzimenti +2
Knot mosaics were introduced by Kauffman and Lomonaco in the context of quantum knots, but have since been studied for their own right. A classical knot mosaic is formed on a squar…
math.GT2024
Bounds on the mosaic number of Legendrian Knots
Margaret Kipe, Samantha Pezzimenti, Leif Schaumann +2
Mosaic tiles were first introduced by Lomonaco and Kauffman in 2008 to describe quantum knots, and have since been studied for their own right. Using a modified set of tiles, front…
math.GT2011
Minimal Degree Parameterizations of the Trefoil and Figure-Eight Knots
Samantha Pezzimenti
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 se…