@article{steel2023interior,
  author  = {Steel, Mike},
  title   = {Interior operators and their relationship to autocatalytic networks},
  journal = {Acta Biotheoretica},
  volume  = {71},
  number  = {4},
  pages   = {21},
  year    = {2023},
  doi     = {10.1007/s10441-023-09472-8},
  note    = {arXiv:2305.16714}
}

@article{lozin2024union,
  author  = {Lozin, Vadim and Zamaraev, Viktor},
  title   = {Union-closed sets and {H}orn {B}oolean functions},
  journal = {Journal of Combinatorial Theory, Series A},
  volume  = {202},
  pages   = {105818},
  year    = {2024},
  doi     = {10.1016/j.jcta.2023.105818}
}

@article{steel2019autocatalytic,
  author  = {Steel, Mike and Hordijk, Wim and Xavier, Joana C.},
  title   = {Autocatalytic networks in biology: structural theory and algorithms},
  journal = {Journal of the Royal Society Interface},
  volume  = {16},
  number  = {151},
  pages   = {20180808},
  year    = {2019},
  doi     = {10.1098/rsif.2018.0808}
}

@article{hordijk2004detecting,
  author  = {Hordijk, Wim and Steel, Mike},
  title   = {Detecting autocatalytic, self-sustaining sets in chemical reaction systems},
  journal = {Journal of Theoretical Biology},
  volume  = {227},
  number  = {4},
  pages   = {451--461},
  year    = {2004},
  doi     = {10.1016/j.jtbi.2003.11.020}
}

@article{hordijk2017chasing,
  author  = {Hordijk, Wim and Steel, Mike},
  title   = {Chasing the tail: the emergence of autocatalytic networks},
  journal = {BioSystems},
  volume  = {152},
  pages   = {1--10},
  year    = {2017},
  doi     = {10.1016/j.biosystems.2016.12.002}
}

@article{mossel2005random,
  author  = {Mossel, Elchanan and Steel, Mike},
  title   = {Random biochemical networks: the probability of self-sustaining autocatalysis},
  journal = {Journal of Theoretical Biology},
  volume  = {233},
  number  = {3},
  pages   = {327--336},
  year    = {2005},
  doi     = {10.1016/j.jtbi.2004.10.011}
}

@article{kauffman1986autocatalytic,
  author  = {Kauffman, Stuart A.},
  title   = {Autocatalytic sets of proteins},
  journal = {Journal of Theoretical Biology},
  volume  = {119},
  number  = {1},
  pages   = {1--24},
  year    = {1986},
  doi     = {10.1016/S0022-5193(86)80047-9}
}

@book{kauffman1993origins,
  author    = {Kauffman, Stuart A.},
  title     = {The Origins of Order: Self-Organization and Selection in Evolution},
  publisher = {Oxford University Press},
  address   = {New York},
  year      = {1993}
}

@incollection{frankl1995extremal,
  author    = {Frankl, Peter},
  title     = {Extremal set systems},
  booktitle = {Handbook of Combinatorics},
  editor    = {Graham, Ronald L. and Gr{\"o}tschel, Martin and Lov{\'a}sz, L{\'a}szl{\'o}},
  volume    = {2},
  pages     = {1293--1329},
  publisher = {Elsevier},
  address   = {Amsterdam},
  year      = {1995}
}

@article{bruhn2015journey,
  author  = {Bruhn, Henning and Schaudt, Oliver},
  title   = {The journey of the union-closed sets conjecture},
  journal = {Graphs and Combinatorics},
  volume  = {31},
  number  = {6},
  pages   = {2043--2074},
  year    = {2015},
  doi     = {10.1007/s00373-014-1515-0}
}

@article{sarvate1989union,
  author  = {Sarvate, Dinesh G. and Renaud, Jean-Claude},
  title   = {On the union-closed sets conjecture},
  journal = {Ars Combinatoria},
  volume  = {27},
  pages   = {149--154},
  year    = {1989}
}

@article{poonen1992union,
  author  = {Poonen, Bjorn},
  title   = {Union-closed families},
  journal = {Journal of Combinatorial Theory, Series A},
  volume  = {59},
  number  = {2},
  pages   = {253--268},
  year    = {1992},
  doi     = {10.1016/0097-3165(92)90068-6}
}

@article{reimer2003average,
  author  = {Reimer, David},
  title   = {An average set size theorem},
  journal = {Combinatorics, Probability and Computing},
  volume  = {12},
  number  = {1},
  pages   = {89--93},
  year    = {2003},
  doi     = {10.1017/S0963548302005230}
}

@article{wojcik1999union,
  author  = {W{\'o}jcik, Piotr},
  title   = {Union-closed families of sets},
  journal = {Discrete Mathematics},
  volume  = {199},
  number  = {1--3},
  pages   = {173--182},
  year    = {1999},
  doi     = {10.1016/S0012-365X(98)00208-8}
}

@misc{gilmer2022constant,
  author = {Gilmer, Justin},
  title  = {A constant lower bound for the union-closed sets conjecture},
  year   = {2022},
  note   = {arXiv:2211.09055}
}

@misc{alweiss2022improved,
  author = {Alweiss, Ryan and Huang, Brice and Sellke, Mark},
  title  = {Improved lower bound for {F}rankl's union-closed sets conjecture},
  year   = {2022},
  note   = {arXiv:2211.11731}
}

@misc{chase2022approximate,
  author = {Chase, Zachary and Lovett, Shachar},
  title  = {Approximate union closed conjecture},
  year   = {2022},
  note   = {arXiv:2211.11689}
}

@misc{sawin2022improved,
  author = {Sawin, Will},
  title  = {An improved lower bound for the union-closed set conjecture},
  year   = {2022},
  note   = {arXiv:2211.11504}
}

@misc{cambie2022better,
  author = {Cambie, Stijn},
  title  = {Better bounds for the union-closed sets conjecture using the entropy approach},
  year   = {2022},
  note   = {arXiv:2212.12500}
}

@book{korte1991greedoids,
  author    = {Korte, Bernhard and Lov{\'a}sz, L{\'a}szl{\'o} and Schrader, Rainer},
  title     = {Greedoids},
  series    = {Algorithms and Combinatorics},
  volume    = {4},
  publisher = {Springer},
  address   = {Berlin},
  year      = {1991}
}

@article{dilworth1940lattices,
  author  = {Dilworth, Robert P.},
  title   = {Lattices with unique irreducible decompositions},
  journal = {Annals of Mathematics},
  volume  = {41},
  number  = {4},
  pages   = {771--777},
  year    = {1940},
  doi     = {10.2307/1968857}
}

@inproceedings{demoura2021lean,
  author    = {de Moura, Leonardo and Ullrich, Sebastian},
  title     = {The {L}ean 4 theorem prover and programming language},
  booktitle = {Automated Deduction -- CADE 28},
  series    = {Lecture Notes in Computer Science},
  volume    = {12699},
  pages     = {625--635},
  publisher = {Springer},
  year      = {2021},
  doi       = {10.1007/978-3-030-79876-5_37}
}

@inproceedings{mathlib2020,
  author    = {{The mathlib Community}},
  title     = {The {L}ean mathematical library},
  booktitle = {Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP 2020)},
  pages     = {367--381},
  publisher = {ACM},
  year      = {2020},
  doi       = {10.1145/3372885.3373824}
}