16 citations · 18 across the 9 of their papers we have counts for
4 papers · 1 filter
Hard unknots are often easy from a different perspective
Jason Cantarella, Henrik Schumacher, Clayton Shonkwiler
Recent attempts to train AI models to recognize knots have produced millions of "hard" unknot diagrams resistant to simplification by Reidemeister moves, pass moves, or random walk…
New Upper Bounds for Stick Numbers
Jason Cantarella, Andrew Rechnitzer, Henrik Schumacher +1
We use a version of simulated annealing with knot-type preserving moves to find polygonal representatives of various knot types with low stick number. These give better bounds on s…
Performance of the Uniform Closure Method for open knotting as a Bayes-type classifier
Emily Tibor, Elizabeth M. Annoni, Erin Brine-Doyle +5
The discovery of knotting in proteins and other macromolecular chains has motivated researchers to more carefully consider how to identify and classify knots in open arcs. Most def…
Knots with Exactly 10 Sticks
Ryan Blair, Thomas D. Eddy, Nathaniel Morrison +1
We prove that the knots and both have stick number 10. These are the first non-torus prime knots with more than 9 crossings for which the exact stick num…