@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} } @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{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{steel2020structure, author = {Steel, Mike and Xavier, Joana C. and Huson, Daniel H.}, title = {The structure of autocatalytic networks, with application to early biochemistry}, journal = {Journal of the Royal Society Interface}, volume = {17}, number = {171}, pages = {20200488}, year = {2020}, doi = {10.1098/rsif.2020.0488} } @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} } @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{hordijk2015algorithms, author = {Hordijk, Wim and Smith, Joshua I. and Steel, Mike}, title = {Algorithms for detecting and analysing autocatalytic sets}, journal = {Algorithms for Molecular Biology}, volume = {10}, pages = {15}, year = {2015}, doi = {10.1186/s13015-015-0042-8} } @article{hordijk2018life, author = {Hordijk, Wim and Steel, Mike}, title = {Autocatalytic networks at the basis of life's origin and organization}, journal = {Life}, volume = {8}, number = {4}, pages = {62}, year = {2018}, doi = {10.3390/life8040062} } @article{xavier2020autocatalytic, author = {Xavier, Joana C. and Hordijk, Wim and Kauffman, Stuart and Steel, Mike and Martin, William F.}, title = {Autocatalytic chemical networks at the origin of metabolism}, journal = {Proceedings of the Royal Society B}, volume = {287}, number = {1922}, pages = {20192377}, year = {2020}, doi = {10.1098/rspb.2019.2377} } @article{gabora2017autocatalytic, author = {Gabora, Liane and Steel, Mike}, title = {Autocatalytic networks in cognition and the origin of culture}, journal = {Journal of Theoretical Biology}, volume = {431}, pages = {87--95}, year = {2017}, doi = {10.1016/j.jtbi.2017.07.022} } @article{loutchko2023algebraic, author = {Loutchko, Dimitri}, title = {An algebraic characterization of self-generating chemical reaction networks using semigroup models}, journal = {Journal of Mathematical Biology}, volume = {86}, pages = {76}, year = {2023}, doi = {10.1007/s00285-023-01899-4} } @article{dittrich2007chemical, author = {Dittrich, Peter and Speroni di Fenizio, Pietro}, title = {Chemical organisation theory}, journal = {Bulletin of Mathematical Biology}, volume = {69}, number = {4}, pages = {1199--1231}, year = {2007}, doi = {10.1007/s11538-006-9130-8} } @article{edelman1985theory, author = {Edelman, Paul H. and Jamison, Robert E.}, title = {The theory of convex geometries}, journal = {Geometriae Dedicata}, volume = {19}, number = {3}, pages = {247--270}, year = {1985}, doi = {10.1007/BF00149365} } @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} } @incollection{korte1984shelling, author = {Korte, Bernhard and Lov{\'a}sz, L{\'a}szl{\'o}}, title = {Shelling structures, convexity and a happy end}, booktitle = {Graph Theory and Combinatorics}, editor = {Bollob{\'a}s, B{\'e}la}, publisher = {Academic Press}, address = {London}, pages = {219--232}, year = {1984} } @incollection{bjorner1992greedoids, author = {Bj{\"o}rner, Anders and Ziegler, G{\"u}nter M.}, title = {Introduction to greedoids}, booktitle = {Matroid Applications}, editor = {White, Neil}, series = {Encyclopedia of Mathematics and its Applications}, volume = {40}, publisher = {Cambridge University Press}, pages = {284--357}, year = {1992} } @article{dietrich1987circuit, author = {Dietrich, Brenda L.}, title = {A circuit set characterization of antimatroids}, journal = {Journal of Combinatorial Theory, Series B}, volume = {43}, number = {3}, pages = {314--321}, year = {1987}, doi = {10.1016/0095-8956(87)90007-4} } @article{dietrich1989survey, author = {Dietrich, Brenda L.}, title = {Matroids and antimatroids---a survey}, journal = {Discrete Mathematics}, volume = {78}, number = {3}, pages = {223--237}, year = {1989}, doi = {10.1016/0012-365X(89)90180-5} } @article{kempner2003correspondence, author = {Kempner, Yulia and Levit, Vadim E.}, title = {Correspondence between two antimatroid algorithmic characterizations}, journal = {Electronic Journal of Combinatorics}, volume = {10}, pages = {R44}, year = {2003}, doi = {10.37236/1737} } @book{doignon1999knowledge, author = {Doignon, Jean-Paul and Falmagne, Jean-Claude}, title = {Knowledge Spaces}, publisher = {Springer}, address = {Berlin}, year = {1999} } @book{falmagne2011learning, author = {Falmagne, Jean-Claude and Doignon, Jean-Paul}, title = {Learning Spaces: Interdisciplinary Applied Mathematics}, publisher = {Springer}, address = {Berlin}, year = {2011} } @article{yoshikawa2017representation, author = {Yoshikawa, Hiyori and Hirai, Hiroshi and Makino, Kazuhisa}, title = {A representation of antimatroids by {H}orn rules and its application to educational systems}, journal = {Journal of Mathematical Psychology}, volume = {77}, pages = {82--93}, year = {2017}, doi = {10.1016/j.jmp.2016.09.002} } @article{wild2017joy, author = {Wild, Marcel}, title = {The joy of implications, aka pure {H}orn formulas: Mainly a survey}, journal = {Theoretical Computer Science}, volume = {658}, pages = {264--292}, year = {2017}, doi = {10.1016/j.tcs.2016.03.018} } @article{balla2013union, author = {Balla, Igor and Bollob{\'a}s, B{\'e}la and Eccles, Tom}, title = {Union-closed families of sets}, journal = {Journal of Combinatorial Theory, Series A}, volume = {120}, number = {3}, pages = {531--544}, year = {2013}, doi = {10.1016/j.jcta.2012.11.001} } @misc{gilmer2022constant, author = {Gilmer, Justin}, title = {A constant lower bound for the union-closed sets conjecture}, howpublished = {arXiv:2211.09055}, year = {2022} } @inproceedings{demoura2021lean4, 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}, publisher = {Springer}, pages = {625--635}, 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)}, publisher = {ACM}, pages = {367--381}, year = {2020}, doi = {10.1145/3372885.3373824} }