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The Tanglenomicon

Zachary Bryhtan, Nicholas Connolly, Isabel Darcy, Ethan Rooke, Joseph Starr*

Mathematics Department at The University of Iowa

Tangle tabulation

"The Most Important Missing Infrastructure Project in Knot Theory"
-Dr. Dror Bar-Natan [2012]

Classified

$\circ$

Rational Tangles

[3 2 2]

$\to$

$+$

Montesinos Tangles

[3 0 ] + [2 1 0] + [2 2 0]

$\to$

$\circ$

Generalized Montesinos Tangles

([3 0] + [3 0] + [2 0]) $\circ$ (1,2)

Not Classified

$+\ \vee$

Algebraic Tangles

([3 2 3] + [3 2 3]) ∨ ([3 2 3] + [3 2 3] )

$\to$

Non-Algebraic Tangles

6* *.[3 2 3 1].[3 2 3 1].[3 2 3 1].[3 2 3 1].[3 2 3 1]

Sources