6 papers
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…
Random knotting in very long off-lattice self-avoiding polygons
Jason Cantarella, Tetsuo Deguchi, Henrik Schumacher +2
We present experimental results on knotting in off-lattice self-avoiding polygons in the bead-chain model. Using Clisby's tree data structure and the scale-free pivot algorithm, fo…
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…
On the average squared radius of gyration of a family of embeddings of subdivision graphs
Jason Cantarella, Henrik Schumacher, Clayton Shonkwiler
Suppose we have an embedding of a graph created by subdividing the edges of a simpler graph . The edges of can be divided into subsets which…
CoBarS: Fast reweighted sampling for polygon spaces in any dimension
Jason Cantarella, Henrik Schumacher
We present the first algorithm for sampling random configurations of closed -gons with any fixed edgelengths in any dimension which is proved to sample cor…
A faster direct sampling algorithm for equilateral closed polygons and the probability of knotting
Jason Cantarella, Henrik Schumacher, Clayton Shonkwiler
We present a faster direct sampling algorithm for random equilateral closed polygons in three-dimensional space. This method improves on the moment polytope sampling algorithm of C…