English

The KnotMosaics Package for SageMath

Geometric Topology 2026-05-15 v1

Abstract

We introduce KnotMosaics, a SageMath package for constructing, visualizing, and analyzing knot mosaic diagrams. The package represents an n-mosaic as a matrix of standard tile labels and implements the local connectivity rules needed to validate mosaics, trace strands and components, compute planar diagram codes, generate random examples, and construct rational tangle mosaics. The planar diagram interface connects the mosaic representation to existing knot and link software, enabling computations such as Jones polynomials and knot Floer homology checks. We describe the package design, its main algorithms, and representative examples that illustrate how KnotMosaics can support computational exploration in knot mosaic theory.

Cite

@article{arxiv.2605.14189,
  title  = {The KnotMosaics Package for SageMath},
  author = {Mary Y. Deng and Allison K. Henrich and Sean H. Kawano and Andrew R. Tawfeek},
  journal= {arXiv preprint arXiv:2605.14189},
  year   = {2026}
}

Comments

12 pages, 9 figures

R2 v1 2026-07-22T07:11:17.894Z