Counting Knot Mosaics with ALLSAT (Student Abstract)

AAAI 2023 pp. 16284-16285

doi:10.1609/AAAI.V37I13.27002 /aaai/2023/miller2023aaai-counting/

Abstract

Knot mosaics are a model of a quantum knot system. A knot mosaic is a m-by-n grid where each location on the grid may contain any of 11 possible tiles such that the final layout has closed loops. Oh et al. proved a recurrence relation of state matrices to count the number of m-by-n knot mosaics. Our contribution is to use ALLSAT solvers to count knot mosaics and to experimentally try different ways to encode the AT MOST ONE constraint in SAT. We plan to use our SAT method as a tool to list knot mosaics of interest for specific classes of knots.

PDF AAAI Semantic Scholar

Cite

Text

Miller. "Counting Knot Mosaics with ALLSAT (Student Abstract)." AAAI Conference on Artificial Intelligence, 2023. doi:10.1609/AAAI.V37I13.27002

Markdown

[Miller. "Counting Knot Mosaics with ALLSAT (Student Abstract)." AAAI Conference on Artificial Intelligence, 2023.](https://mlanthology.org/aaai/2023/miller2023aaai-counting/) doi:10.1609/AAAI.V37I13.27002

BibTeX

@inproceedings{miller2023aaai-counting,
  title     = {{Counting Knot Mosaics with ALLSAT (Student Abstract)}},
  author    = {Miller, Hannah},
  booktitle = {AAAI Conference on Artificial Intelligence},
  year      = {2023},
  pages     = {16284-16285},
  doi       = {10.1609/AAAI.V37I13.27002},
  url       = {https://mlanthology.org/aaai/2023/miller2023aaai-counting/}
}