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{sheriffquantifying2024,
	title = {Quantifying chemical short-range order in metallic alloys},
	doi = {10.1073/pnas.2322962121},
	journaltitle = {Proceedings of the National Academy of Sciences},
	author = {Sheriff, Killian and Cao, Yifan and Smidt, Tess and Freitas, Rodrigo},
	date = {2024-06-18},
}

and

@article{sheriff2024chemicalmotif,
  title = {Chemical-motif characterization of short-range order with E(3)-equivariant graph neural networks},
  DOI = {10.1038/s41524-024-01393-5},
  journal = {npj Computational Materials},
  author = {Sheriff,  Killian and Cao,  Yifan and Freitas,  Rodrigo},
  year = {2024},
  month = sep,
}