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math.GT2026
Knots and the Sierpinski Tetrahedron
Malors Espinosa
In this paper we prove that there are infinitely many knots that cannot be embedded in the 1-skeletons of the finite iterations of the Sierpinski tetrahedron fractal. We do this by…
math.GT2025
Knots and Coxeter Groups
Dylan Burke, Geoffrey Cuff-Chartrand, Malors Espinosa +2
In this paper we study knots created by galleries in the affine Coxeter complex of type \widewedge{B3}. We bound the stick number by 40 and prove that the smallest length of threef…
math.GT2024
Knots Inside Fractals
Joshua Broden, Malors Espinosa, Noah Nazareth +1
We prove that all knots can be embedded into the Menger Sponge fractal. We prove that all Pretzel knots can be embedded into the Sierpinski Tetrahedron. Then we compare the number…