@article{Newman,
  author = {Newman, Donald J.},
  title = {Tesselation of integers},
  journal = {Journal of Number Theory},
  volume = {9},
  number = {1},
  pages = {107--111},
  year = {1977},
  doi = {10.1016/0022-314X(77)90054-3}
}

@article{Bhattacharya,
  author = {Bhattacharya, Siddhartha},
  title = {Periodicity and decidability of tilings of {$\mathbb{Z}^2$}},
  journal = {American Journal of Mathematics},
  volume = {142},
  number = {1},
  pages = {255--266},
  year = {2020},
  doi = {10.1353/ajm.2020.0006},
  note = {Numbered locators refer to arXiv:1602.05738v1},
  url = {https://arxiv.org/abs/1602.05738v1}
}

@article{GTStructure,
  author = {Greenfeld, Rachel and Tao, Terence},
  title = {The structure of translational tilings in {$\mathbb{Z}^d$}},
  journal = {Discrete Analysis},
  year = {2021},
  note = {Paper No. 16, 28 pp. Numbered locators refer to arXiv:2010.03254v3},
  doi = {10.19086/da.28324},
  url = {https://arxiv.org/abs/2010.03254v3}
}

@article{GTPeriodic,
  author = {Greenfeld, Rachel and Tao, Terence},
  title = {A counterexample to the periodic tiling conjecture},
  journal = {Annals of Mathematics},
  volume = {200},
  number = {1},
  pages = {301--363},
  year = {2024},
  note = {Numbered locators refer to arXiv:2211.15847v3},
  doi = {10.4007/annals.2024.200.1.5},
  url = {https://arxiv.org/abs/2211.15847v3}
}

@article{GTUndecidable,
  author = {Greenfeld, Rachel and Tao, Terence},
  title = {Undecidability of translational monotilings},
  journal = {Journal of the European Mathematical Society},
  year = {2025},
  note = {Published online first. Numbered locators refer to arXiv:2309.09504v2},
  doi = {10.4171/JEMS/1673},
  url = {https://arxiv.org/abs/2309.09504v2}
}

@article{MSSReduction,
  author = {Meyerovitch, Tom and Sanadhya, Shrey and Solomon, Yaar},
  title = {A note on reduction of tiling problems},
  journal = {Israel Journal of Mathematics},
  volume = {267},
  pages = {421--435},
  year = {2025},
  note = {Numbered locators refer to arXiv:2211.07140v1},
  doi = {10.1007/s11856-025-2716-3},
  url = {https://arxiv.org/abs/2211.07140v1}
}


@article{GTTwoTiles,
  author = {Greenfeld, Rachel and Tao, Terence},
  title = {Undecidable translational tilings with only two tiles, or one nonabelian tile},
  journal = {Discrete \& Computational Geometry},
  volume = {70},
  number = {4},
  pages = {1652--1706},
  year = {2023},
  doi = {10.1007/s00454-022-00426-4},
  note = {Numbered locators refer to arXiv:2108.07902v3},
  url = {https://arxiv.org/abs/2108.07902v3}
}


@article{LagariasWang,
  author = {Lagarias, Jeffrey C. and Wang, Yang},
  title = {Tiling the line with translates of one tile},
  journal = {Inventiones Mathematicae},
  volume = {124},
  pages = {341--365},
  year = {1996},
  doi = {10.1007/s002220050056}
}

@article{WijshoffVanLeeuwen,
  author = {Wijshoff, H. A. G. and van Leeuwen, J.},
  title = {Arbitrary versus periodic storage schemes and tessellations of the plane using one type of polyomino},
  journal = {Information and Control},
  volume = {62},
  number = {1},
  pages = {1--25},
  year = {1984},
  doi = {10.1016/S0019-9958(84)80007-8}
}

@article{RationalPolygons,
  author = {de Dios Pont, Jaume and Greb{\'i}k, Jan and Greenfeld, Rachel and Madrid, Jos{\'e}},
  title = {Periodicity and decidability of translational tilings by rational polygonal sets},
  journal = {Expositiones Mathematicae},
  volume = {44},
  number = {1},
  pages = {125620},
  year = {2026},
  doi = {10.1016/j.exmath.2024.125620},
  note = {Numbered locators refer to arXiv:2408.02151v2},
  url = {https://arxiv.org/abs/2408.02151v2}
}