knot theory, confined knot, extreme confinement
This data set consists of knot configurations (which are designed to model knotting in extreme confinement) and their corresponding knot types. The configurations lie within a cylinder with radius one and height one, with vertices alternating between the top and bottom disks. The vertices are chosen uniformly with respect to area on the endcap disks. Due to this construction, the set of knot types is independent of radius or height in the construction. In particular, given one such configuration, the act of stretching/shrinking the cylinder radius and/or height does not pass edges through each other. Thus, the knot type is fixed. By setting the height to one and decreasing the radius to nearly 0, one obtains configurations that approach being equilateral (with unit length edges) and under extreme confinement. The data set consists of 1,000,000 configurations for six through 30 edges by steps of two and their knot types (both as plain text files). More details about the construction and available files are available in the README.txt file in the zip file. Also, see the corresponding paper: Knotting spectrum of polygonal knots in extreme confinement. Claus Ernst, Eric J. Rawdon, and Uta Ziegler. This material is based upon work supported by the National Science Foundation under Grant Nos. 1418869 and 1720342 to Eric J. Rawdon. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
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