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math.GT2022
The ropelength conjecture of alternating knots
Yuanan Diao
A long standing conjecture states that the ropelength of any alternating knot is at least proportional to its crossing number. In this paper we prove that this conjecture is true.…
math.GT2022
The average genus of oriented rational links with a given crossing number
Dawn Ray, Yuanan Diao
In this paper, we enumerate the number of oriented rational knots and the number of oriented rational links with any given crossing number and minimum genus. This allows us to obta…