4 citations · 5 across the 6 of their papers we have counts for
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 wa…
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…