11 citations · 30 across the 16 of their papers we have counts for
4 papers · 1 filter
Tight Bounds for Tight Links: Ropelength of T(Q,Q) torus links
Alexander R. Klotz
Ropelength, L, is a parameter characterizing the minimum contour length of a knot or link. There exist upper and lower bounds on ropelength with respect to crossing number, C, incl…
Ropelength and writhe quantization of 12-crossing knots
Alexander R. Klotz, Caleb J. Anderson
The ropelength of a knot is the minimum length required to tie it. Computational upper bounds have previously been computed for every prime knot with up to 11 crossings. Here, we p…
The tightest knot is not necessarily the smallest
Alexander R. Klotz
In this note, we attempt to find counterexamples to the conjecture that the ideal form of a knot, that which minimizes its contour length while respecting a no-overlap constraint,…
The Ropelength of Complex Knots
Alexander R. Klotz, Matthew Maldonado
The ropelength of a knot is the minimum contour length of a tube of unit radius that traces out the knot in three dimensional space without self-overlap, colloquially the minimum a…