@article{vanDerWaerden1927,
  author  = {van der Waerden, B. L.},
  title   = {Beweis einer {Baudetschen} {Vermutung}},
  journal = {Nieuw Archief voor Wiskunde (2)},
  volume  = {15},
  pages   = {212--216},
  year    = {1927},
  url     = {https://resolver.kb.nl/resolve?urn=MMKWG01:022157001:00228}
}

@article{vanDerWaerden1998,
  author  = {van der Waerden, B. L.},
  title   = {{Wie der Beweis der Vermutung von Baudet gefunden wurde}},
  journal = {Elemente der Mathematik},
  volume  = {53},
  pages   = {139--148},
  year    = {1998},
  note    = {Reprint of the 1965 article},
  url     = {https://ems.press/content/serial-article-files/45097}
}

@incollection{stanley2007,
  author    = {Stanley, Richard P.},
  title     = {An introduction to hyperplane arrangements},
  booktitle = {Geometric Combinatorics},
  series    = {IAS/Park City Mathematics Series},
  volume    = {13},
  pages     = {389--496},
  publisher = {American Mathematical Society},
  address   = {Providence, RI},
  year      = {2007},
  url       = {https://www.cis.upenn.edu/~cis6100/sp06stanley.pdf}
}

@article{erdos1980,
  author  = {Erd{\H{o}}s, Paul},
  title   = {A survey of problems in combinatorial number theory},
  journal = {Annals of Discrete Mathematics},
  volume  = {6},
  pages   = {89--115},
  year    = {1980},
  doi     = {10.1016/S0167-5060(08)70697-6},
  url     = {https://www.renyi.hu/~p_erdos/1980-03.pdf},
  note    = {\href{https://doi.org/10.1016/S0167-5060(08)70697-6}{doi:10.1016/S0167-5060(08)70697-6}}
}

@incollection{erdosLovasz1975,
  author    = {Erd{\H{o}}s, Paul and Lov{\'a}sz, L{\'a}szl{\'o}},
  title     = {Problems and results on {$3$}-chromatic hypergraphs and some related questions},
  booktitle = {Infinite and Finite Sets, Vol.~II},
  series    = {Colloquia Mathematica Societatis J{\'a}nos Bolyai},
  volume    = {10},
  pages     = {609--627},
  publisher = {North-Holland},
  address   = {Amsterdam},
  year      = {1975},
  url       = {https://www.renyi.hu/~p_erdos/1975-34.pdf}
}

@misc{foxHunter2026,
  author        = {Fox, Jacob and Hunter, Zach},
  title         = {Three-color {van der Waerden} numbers grow super-exponentially},
  year          = {2026},
  eprint        = {2606.02541},
  archivePrefix = {arXiv},
  primaryClass  = {math.CO},
  doi           = {10.48550/arXiv.2606.02541},
  url           = {https://arxiv.org/abs/2606.02541v1},
  note          = {\href{https://arxiv.org/abs/2606.02541v1}{arXiv:2606.02541v1}, submitted June 1, 2026}
}

@misc{camposFoxSchildkraut2026,
  author        = {Campos, Marcelo and Fox, Jacob and Schildkraut, Carl},
  title         = {A new lower bound for two-color {van der Waerden} numbers},
  year          = {2026},
  eprint        = {2608.20824},
  archivePrefix = {arXiv},
  primaryClass  = {math.CO},
  doi           = {10.48550/arXiv.2608.20824},
  url           = {https://arxiv.org/abs/2608.20824v1},
  note          = {\href{https://arxiv.org/abs/2608.20824v1}{arXiv:2608.20824v1}, submitted August 21, 2026}
}

@misc{shiDong2026,
  author        = {Shi, Ruizhe and Dong, Yiqi},
  title         = {An improved upper bound for colorings without symmetrically colored {$k$}-term arithmetic progressions},
  year          = {2026},
  eprint        = {2607.20752},
  archivePrefix = {arXiv},
  primaryClass  = {math.CO},
  doi           = {10.48550/arXiv.2607.20752},
  url           = {https://arxiv.org/abs/2607.20752v2},
  note          = {\href{https://arxiv.org/abs/2607.20752v2}{arXiv:2607.20752v2}, revised July 28, 2026}
}

@article{erdosRado1952,
  author = {Erd{\H{o}}s, Paul and Rado, Richard},
  title = {Combinatorial theorems on classifications of subsets of a given set},
  journal = {Proceedings of the London Mathematical Society (3)},
  volume = {2},
  pages = {417--439},
  year = {1952},
  doi = {10.1112/plms/s3-2.1.417},
  url = {https://www.renyi.hu/~p_erdos/1952-02.pdf}
}

@article{schmidt1962,
  author = {Schmidt, Wolfgang M.},
  title = {Two combinatorial theorems on arithmetic progressions},
  journal = {Duke Mathematical Journal},
  volume = {29},
  pages = {129--140},
  year = {1962},
  doi = {10.1215/S0012-7094-62-02914-9}
}

@article{berlekamp1968,
  author = {Berlekamp, Elwyn R.},
  title = {A construction for partitions which avoid long arithmetic progressions},
  journal = {Canadian Mathematical Bulletin},
  volume = {11},
  number = {3},
  pages = {409--414},
  year = {1968},
  doi = {10.4153/CMB-1968-047-7}
}

@article{szabo1990,
  author = {Szab{\'o}, Zolt{\'a}n},
  title = {An application of {Lov{\'a}sz}' local lemma---A new lower bound for the {van der Waerden} number},
  journal = {Random Structures \& Algorithms},
  volume = {1},
  number = {3},
  pages = {343--360},
  year = {1990},
  doi = {10.1002/rsa.3240010307}
}

@article{kozikShabanov2016,
  author = {Kozik, Jakub and Shabanov, Dmitry},
  title = {Improved algorithms for colorings of simple hypergraphs and applications},
  journal = {Journal of Combinatorial Theory, Series B},
  volume = {116},
  pages = {312--332},
  year = {2016},
  doi = {10.1016/j.jctb.2015.09.004}
}

@article{hunter2025,
  author = {Hunter, Zach},
  title = {Lower bounds for multicolor {van der Waerden} numbers},
  journal = {Israel Journal of Mathematics},
  volume = {267},
  pages = {783--795},
  year = {2025},
  doi = {10.1007/s11856-025-2735-0}
}

@article{shelah1988,
  author = {Shelah, Saharon},
  title = {Primitive recursive bounds for {van der Waerden} numbers},
  journal = {Journal of the American Mathematical Society},
  volume = {1},
  number = {3},
  pages = {683--697},
  year = {1988},
  doi = {10.1090/S0894-0347-1988-0929498-X}
}

@article{gowers2001,
  author = {Gowers, W. T.},
  title = {A new proof of {Szemer{\'e}di}'s theorem},
  journal = {Geometric and Functional Analysis},
  volume = {11},
  number = {3},
  pages = {465--588},
  year = {2001},
  doi = {10.1007/s00039-001-0332-9}
}

@misc{openaiArithmeticProgressions2026,
  author = {{OpenAI}},
  title = {{Quasipolynomial Bounds for Arithmetic Progressions}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Quasipolynomial-Bounds-for-Arithmetic-Progressions-September-23-2026/paper.pdf}{OAI:Quasipolynomial-Bounds-for-Arithmetic-Progressions-September-23-2026}},
  year = {2026}
}

@article{behrend1946,
  author = {Behrend, F. A.},
  title = {On sets of integers which contain no three terms in arithmetical progression},
  journal = {Proceedings of the National Academy of Sciences of the United States of America},
  volume = {32},
  number = {12},
  pages = {331--332},
  year = {1946},
  doi = {10.1073/pnas.32.12.331}
}

@article{green2022,
  author = {Green, Ben},
  title = {New lower bounds for {van der Waerden} numbers},
  journal = {Forum of Mathematics, Pi},
  volume = {10},
  pages = {e18, 1--51},
  year = {2022},
  doi = {10.1017/fmp.2022.12}
}

@incollection{greenWolf2010,
  author = {Green, Ben and Wolf, Julia},
  title = {A note on {Elkin}'s improvement of {Behrend}'s construction},
  booktitle = {Additive Number Theory},
  pages = {141--144},
  publisher = {Springer},
  year = {2010},
  doi = {10.1007/978-0-387-68361-4_9}
}

@article{hunter2022,
  author = {Hunter, Zach},
  title = {Improved lower bounds for {van der Waerden} numbers},
  journal = {Combinatorica},
  volume = {42},
  pages = {1231--1252},
  year = {2022},
  doi = {10.1007/s00493-022-4925-2}
}

@article{rankin1961,
  author = {Rankin, R. A.},
  title = {Sets of integers containing not more than a given number of terms in arithmetical progression},
  journal = {Proceedings of the Royal Society of Edinburgh, Section A},
  volume = {65},
  number = {4},
  pages = {332--344},
  year = {1961},
  doi = {10.1017/S0080454100017726},
  note = {\href{https://doi.org/10.1017/S0080454100017726}{doi:10.1017/S0080454100017726}}
}

@article{erdosTuran1936,
  author = {Erd{\H{o}}s, Paul and Tur{\'a}n, Paul},
  title = {On some sequences of integers},
  journal = {Journal of the London Mathematical Society},
  volume = {s1-11},
  number = {4},
  pages = {261--264},
  year = {1936},
  doi = {10.1112/jlms/s1-11.4.261},
  note = {\href{https://doi.org/10.1112/jlms/s1-11.4.261}{doi:10.1112/jlms/s1-11.4.261}}
}

@misc{kelleyMeka2023,
  author = {Kelley, Zander and Meka, Raghu},
  title = {Strong bounds for {$3$}-progressions},
  year = {2023},
  eprint = {2302.05537v6},
  archivePrefix = {arXiv},
  primaryClass = {math.NT},
  note = {Author version \href{https://arxiv.org/abs/2302.05537v6}{arXiv:2302.05537v6}, revised October 28, 2024}
}

@misc{lengSahSawhney2024,
  author = {Leng, James and Sah, Ashwin and Sawhney, Mehtaab},
  title = {Improved bounds for {Szemer{\'e}di}'s theorem},
  year = {2024},
  eprint = {2402.17995v2},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  note = {\href{https://arxiv.org/abs/2402.17995v2}{arXiv:2402.17995v2}, revised February 29, 2024}
}