Polya

A python implementation of Polya's enumeration theory and pattern inventory formula.

Usage

Here is an example on how to extract the cycle index polynomial (p_g) and number of distinct first coordination polyhedron (nms) for the fcc crystal structure with a number of ntypes = 3 chemical elements. Additonal graph geometries can be defined in polya/_src/graphs.py. This example can be found in the examples/ folder.

from polya import Polya
pl = Polya(graph_name="fcc")
p_g, nms = pl.get_gt(ntypes=3)
print(p_g)

Installation

For a standalone Python package or Conda environment, please use:

pip install --user polyaenum

If you want to install the lastest git commit, please replace polya by git+https://github.com/killiansheriff/polya.git.

Contact

If any questions, feel free to contact me (ksheriff at mit dot edu).

References & Citing

If you use this repository in your work, please cite:

@article{sheriff2023quantifying,
  title={Quantifying chemical short-range order in metallic alloys},
  author={Sheriff, Killian and Cao, Yifan and Smidt, Tess and Freitas, Rodrigo},
  journal={arXiv},
  year={2023},
  doi={10.48550/arXiv.2311.01545}
}

and

@article{sheriff2024chemicalmotif,
  title={Chemical-motif characterization of short-range order with E(3)-equivariant graph neural networks}, 
  author={Killian Sheriff and Yifan Cao and Rodrigo Freitas},
  journal={arXiv},
  year={2024},
  doi={10.48550/arXiv.2405.08628}