Abstract
Abstract
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 Cantarella et al (2016 J. Phys. A: Math. Theor.
49 275202) and has (expected) time per sample quadratic in the number of edges in the polygon. We use our new sampling method and a new code for computing invariants based on the Alexander polynomial to investigate the probability of finding unknots among equilateral closed polygons.
Funder
Simons Foundation
National Science Foundation
Reference38 articles.
1. The generation of random equilateral polygons;Alvarado;J. Stat. Phys.,2011
2. An approximate minimum degree ordering algorithm;Amestoy;SIAM J. Matrix Anal. Appl.,1996
3. Algorithm 837: AMD, an approximate minimum degree ordering algorithm;Amestoy;ACM Trans. Math. Softw.,2004
4. plCurve: fast polygon library;Ashton,2001–2024